Image data generation with reduced amount of processing

ABSTRACT

An image data generator for generating data on a size reduced image of an original image. In one embodiment, the image data generator includes: an inverse wavelet transform unit to perform on inverse wavelet transform on wavelet coefficients; and a coefficient selecting unit to select, of wavelet coefficients in a sub-band, wavelet coefficients to be subjected to the inverse wavelet transform. In one embodiment, the inverse wavelet transform unit performs the inverse wavelet transform only on the wavelet coefficients selected in the coefficient selecting unit with respect to the wavelet coefficients in the sub-band.

The present application claims priority to the corresponding Japanesepriority application 2002-072696 filed on Mar. 15, 2002, the entirecontents of which are hereby incorporated by reference.

FIELD OF THE INVENTION

The present invention generally relates to image data generators, andmore particularly to an image data generator for generating a reducedsize image of an original. For purpose of this application, a reducedsize image can be the one whose aspect ratio is different from that ofthe original image. The present invention is applicable to anapplication program for generating a reduced size image of an original,a device driver such as a printer driver, and other apparatuses forprocessing images.

DESCRIPTION OF THE RELATED ART

Wavelet transforms have been employed more often lately as a substitutefrequency conversion technique for DCTs (Discrete Cosine Transforms)employed in JPEG (Joint Photographic Coding Experts Group). A typicalexample of the use of wavelet transforms is JPEG 2000, which is an imagecompression and decompression method standardized internationally in2001 as a successor to JPEG.

A wavelet transform is characterized in that an image is compressed athigh compression rates with excellent image quality, and at the time ofcompression, is decomposed into a plurality of resolution components sothat an image having a lower resolution than the original image isgenerated.

Conventionally, however, the following restriction exists in generatinga low-resolution image from the original image. According to theconventional wavelet decoding entailing resolution conversion,resolution can be reduced only to 1/2^(n) (n=1, 2 . . . ) due to thenature of the wavelet decoding. This is because the conventional wavelettransform employs a two-division filter bank. Accordingly, thelow-frequency components can be synthesized only in 1/2^(n) in asynthesis filter bank in the process of decoding, so that the reductionrate of the decoded image is limited to 1/2^(n).

On the other hand, there is a demand for decoding with resolutions otherthan 1/2^(n) increases as the original image has a higher resolution.That is, if decoding can be performed with resolutions of any rationalnumbers including 1/2^(n), the decoding is independent of theconstraints on the terminal side, thereby considerably expanding itsapplication range.

With respect to this resolution conversion, Japanese Laid-Open PatentApplications No. 2000-125293 and No. 2000-125294 (hereinafter referredto as first prior art and second prior art, respectively), showing theabove-described problem in resolution conversion, disclose waveletdecoders and methods. Those wavelet decoders and methods are allowed todecode an image signal compressed and coded by wavelet transforms withresolutions of any rational numbers without being affected by theconstraints on the terminal side. As a result, those wavelet decodersand methods are allowed to effectively store and display, for instance,a so-called thumbnail, which is frequently used in electronic stillcameras and printers, and an image obtained by converting the resolutionof an original image (a reduced or enlarged original image). Therefore,those wavelet decoders and methods can be applied to a wider variety ofproducts.

Each of the wavelet decoders in the first prior art and the second priorart includes an entropy decoding unit that applies entropy decoding to acoded bit stream, an inverse quantization unit that inversely quantizesquantization coefficients and outputs transform coefficients, atransform coefficient inverse scanning unit that scans the transformcoefficients according to a predetermined method and rearranges thetransform coefficients, and a wavelet inverse transform unit thatinversely transforms the rearranged transform coefficients and providesa decoded image. The wavelet inverse transform unit includes means forlimiting the bandwidth of the transform coefficients in accordance withmagnifications of resolution conversion, and has a configuration whereup-samplers, down-samplers, and synthesis filers are adaptivelyarranged.

FIG. 1 is a diagram showing the configuration of the wavelet inversetransform unit of the wavelet decoder of the second prior art in thecase of obtaining a 1/3 resolution of an original image. The waveletinverse transform unit of FIG. 1 includes 2× up-samplers 119, 121, 124,126, 129 and 131, low-pass filters 120, 125, and 130 for synthesis,high-pass filters 122, 127, and 132 for synthesis, adders 123, and adown-sampler 134. Due to band restriction, the coefficients ofresolution components (LH signal and H signal) 111 and 112 higher thanone third of the resolution of the original image are not employed. Onthe other hand, the coefficient of low-resolution components (LLL signaland LLH signal) 109 and 110 are combined and output from the adder 123further to be inversely converted, so that an image (signal) 114 whoseresolution is a half of the resolution of the original image isobtained. The signal 114 is further inversely transformed so that animage (signal) 117 that has the same resolution as the original image isobtained. Finally, the signal 117 is thinned out or reduced to one thirdby the down-sampler 134 so that a desired image (signal) 118 isobtained. In FIG. 1, the elements indicated by the broken lines areunnecessary.

Thus, in both of the first prior art and the second prior art describedabove, it is not clear what “configuration where . . . are adaptivelyarranged” means. In the embodiments of those inventions, wavelettransform is performed after band restriction so that a decoded image isobtained. Thereafter, the decoded image is thinned out by thedown-sampler provided at the final stage, so that a reduced image isobtained. Such a configuration, however, does not also perform inversewavelet transform and decoding on pixels that are finally eliminated,and therefore, lacks efficiency

Japanese Laid-Open Patent Applications No. 2002-152517, No. 2002-152744,and No. 2002-344732 disclose an apparatus and methods for obtaining adecompressed image from a coded image. In these inventions, waveletcoefficients of up to a resolution level close to a desired size areextracted to be subjected to inverse wavelet transform so that a decodedimage is generated. Thereafter, processing for varying magnification isperformed so that an image of the desired size is obtained. In theseinventions, it is required to vary magnification.

Further, the technique of imposing band restriction on a waveletcoefficient in the first prior art and the second prior art may beeffective to some extent in increasing processing speed. This technique,however, is based on the premise that all of the codes of the waveletcoefficients that are not subjected to band restriction are decoded inthe entropy decoding unit, and therefore, is not efficient.

SUMMARY OF THE INVENTION

An image data generation method and apparatus are disclosed. In oneembodiment, an image data generator generates data of a reduced sizeimage of an original image. The image data generator comprises aninverse wavelet transform unit to perform an inverse wavelet transformon wavelet coefficients and a coefficient selecting unit to selectwavelet coefficients in a sub-band, wavelet coefficients to be subjectedto the inverse wavelet transform. The inverse wavelet transform unitperforms the inverse wavelet transform only on the wavelet coefficientsselected in the coefficient selecting unit with respect to the waveletcoefficients in the sub-band.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention willbecome more apparent from the following detailed description when readin conjunction with the accompanying drawings, in which:

FIG. 1 is a diagram showing the configuration of an inverse wavelettransform unit of the prior art in the case of obtaining a1/3-resolution of an original image;

FIG. 2 is a diagram for illustrating a process of two-dimensionally(vertically and horizontally) performing wavelet transform called 5×3transform employed in JPEG 2000 on a 16×16 monochrome image according toone embodiment of the present invention;

FIG. 3 is another diagram for illustrating the process oftwo-dimensionally (vertically and horizontally) performing wavelettransform called 5×3 transform employed in JPEG 2000 on the 16×16monochrome image according to one embodiment of the present invention;

FIG. 4 is another diagram for illustrating the process oftwo-dimensionally (vertically and horizontally) performing wavelettransform called 5×3 transform employed in JPEG 2000 on the 16×16monochrome image according to one embodiment of the present invention;

FIG. 5 is another diagram for illustrating the process oftwo-dimensionally (vertically and horizontally) performing wavelettransform called 5×3 transform employed in JPEG 2000 on the 16×16monochrome image according to one embodiment of the present invention;

FIG. 6 is a diagram showing a typical coefficient array afterrearranging coefficients obtained after two wavelet transform operationsaccording to one embodiment of the present invention;

FIG. 7 is a block diagram showing an image data generator according to afirst embodiment of the present invention;

FIG. 8A is a diagram showing a 16×16 image generated by performinginverse wavelet transform on all coefficients obtained after performing5×3 wavelet transform on the original image of FIG. 2 in the case ofobtaining a 5×5 image, and FIG. 8B is a diagram showing the 16×16 imageof FIG. 8A in the case of obtaining a 5×4 image according to the firstembodiment of the present invention;

FIG. 9 is a diagram showing a 16×16 image generated by performinghorizontal filtering at the time of the inverse wavelet transformoperation on all the coefficients obtained after performing 5×3 wavelettransform on the original image of FIG. 2 in the case of obtaining the5×5 image, and FIG. 9B is a diagram showing the 16×16 image of FIG. 9Ain the case of obtaining the 5×4 image according to the first embodimentof the present invention;

FIG. 10 is a diagram showing a configuration for generating a1/3-resolution image along the flow of wavelet transform and inversewavelet transform according to one embodiment of the present invention;

FIG. 11 is a block diagram for illustrating an image data generatoraccording to a second embodiment of the present invention;

FIG. 12 is a block diagram showing an image data generator according toa third embodiment of the present invention;

FIG. 13 is a block diagram showing another image data generatoraccording to the third embodiment of the present invention;

FIG. 14 is a flowchart for illustrating the basic flow of an operationof generating a reduced size image in an image data generator accordingto a fourth embodiment of the present invention;

FIG. 15 is a diagram showing a code configuration according to thefourth embodiment of the present invention;

FIG. 16 is a diagram showing the relationship between decompositionlevel and resolution level according to the fourth embodiment of thepresent invention;

FIG. 17 is a flowchart for illustrating an LL generating operationperformed on each component according to the fourth embodiment of thepresent invention;

FIG. 18 is a flowchart for illustrating the operation of FIG. 17 indetail according to the fourth embodiment of the present invention;

FIG. 19 is a flowchart for illustrating a horizontal pixel positiondetermining and horizontal filtering operation performed on eachcomponent according to the fourth embodiment of the present invention;

FIG. 20 is a flowchart for illustrating the operation of FIG. 19 indetail according to the fourth embodiment of the present invention;

FIG. 21 is a flowchart for illustrating a vertical pixel positiondetermining and vertical filtering operation performed on each componentaccording to the fourth embodiment of the present invention;

FIG. 22 is a flowchart for illustrating the operation of FIG. 21 indetail according to the fourth embodiment of the present invention;

FIG. 23 is a diagram for illustrating an inverse color conversionoperation according to the fourth embodiment of the present invention;

FIG. 24A is a diagram showing pixels to be obtained in the case ofobtaining a 2/3-resolution image of interleaved coefficients and FIG.24B is a diagram showing pixels to be obtained in the case of generatinga 10×8 image of the interleaved coefficients according to the fourthembodiment of the present invention;

FIG. 25A is another diagram showing the pixels to be obtained in thecase of obtaining the 2/3-resolution image of the interleavedcoefficients and FIG. 25B is another diagram showing the pixels to beobtained in the case of generating the 10×8 image of the interleavedcoefficients according to the fourth embodiment of the presentinvention;

FIG. 26 is a block diagram showing an image data generator according toa fifth embodiment of the present invention;

FIG. 27A is a diagram showing coefficients of a 2LL sub-band, and FIG.27B is a diagram showing the coefficients divided into bit planesaccording to a sixth embodiment of the present invention;

FIG. 28 is a diagram showing a code configuration according to the sixthembodiment of the present invention;

FIG. 29 is a flowchart for illustrating the basic flow of a reduced sizeimage generating operation performed in an image data generatoraccording to the sixth embodiment of the present invention;

FIG. 30 is a flowchart for expatiating partial decoding in the operationof FIG. 29 according to the sixth embodiment of the present invention;

FIG. 31 is another flowchart for expatiating the partial decoding in theoperation of FIG. 29 according to the sixth embodiment of the presentinvention;

FIG. 32 is another flowchart for expatiating the partial decoding in theoperation of FIG. 29 according to the sixth embodiment of the presentinvention; and

FIG. 33 is a flowchart for illustrating the basic flow of anotherreduced size image generating operation performed in the image datagenerator according to the sixth embodiment of the present invention.

DETAILED DESCRIPTION OF THE PRESENT INVENTION

An image data generator and an image data generating method in which theabove-described disadvantages are eliminated is disclosed.

Focusing on the fact that a wavelet coefficient inherently correspondsto its pixel position, one embodiment of the present invention providesan image data generator and an image data generating method that cangenerate decoded image data of a desired resolution, or desired reducedsize image data, with a smaller amount of processing by performinginverse wavelet transform only on the coefficients that are related topixels desired to be finally obtained, using the correspondence betweenthe wavelet coefficients and their pixel positions. As mentioned above,a reduced size image can be the one whose aspect ratio is not equal tothat of the original image.

Another embodiment of the present invention provides an image datagenerator and an image data generating method that can generate decodedimage data of a desired resolution, or desired reduced size image data,balancing a decoding rate and decoding image quality, by timelyperforming partial decoding on coded wavelet coefficients.

Another embodiment of the present invention comprises image datagenerator for generating data on a reduced size image of an originalimage, where the image data generator includes an inverse wavelettransform unit to perform an inverse wavelet transform on waveletcoefficients and a coefficient selecting unit to select waveletcoefficients in a sub-band, wavelet coefficients to be subjected to theinverse wavelet transform, wherein the inverse wavelet transform unitperforms the inverse wavelet transform only on the wavelet coefficientsselected in the coefficient selecting unit with respect to the waveletcoefficients in the sub-band.

Another embodiment of the present invention comprises an image datagenerator for generating data on a reduced size image of an originalimage, where the image data generator includes an inverse wavelettransform unit to perform an inverse wavelet transform on waveletcoefficients of a plurality of components, the inverse wavelet transformunit to perform the inverse wavelet transform independently on each ofthe components with at least one of the components having a resolutionset, which is different from a resolution set for the rest of thecomponents.

Another embodiment of the present invention comprises an image datagenerator for generating data on a reduced size image of an originalimage, where the image data generator includes a coefficient decodingunit to decode codes into which wavelet coefficients are coded and acode omitting unit to omit codes not to be decoded of codes in asub-band, where the coefficient decoding unit decodes codes other thanthose omitted by the code omitting unit.

According to the above-described image data generators of the presentinvention, the wavelet coefficients are subjected to inverse wavelettransform, and in the case of generating a reduced size image of anoriginal image, the wavelet coefficients in the same sub-band areselectively subjected to an inverse wavelet transform. Therefore, thereduced size image can be generated with a reduced amount ofcalculation.

Further, the wavelet coefficients in the same sub-band are partiallydecoded in performing an inverse wavelet transform on the waveletcoefficients and generating a reduced size image of an original image.Therefore, the reduced size image can be generated with decoding speedand decoded image quality being balanced with each other.

In another embodiment of the present invention, a method of generatingdata on a reduced size image of an original image is disclosed, wherethe method includes: (a) selecting, of wavelet coefficients in asub-band, wavelet coefficients to be subjected to an inverse wavelettransform; and (b) performing the inverse wavelet transform on waveletcoefficients, where performing the inverse wavelet transform includesperforming the inverse wavelet transform only on the waveletcoefficients selected to be subjected to the inverse wavelet transformwith respect to the wavelet coefficients in the sub-band.

Another embodiment of the present invention comprises a method ofgenerating data on a reduced size image of an original image, where themethod includes performing an inverse wavelet transform on waveletcoefficients of a plurality of components, wherein the inverse wavelettransform is performed independently on each of the components with atleast one of the components having a resolution set which is differentfrom a resolution set for the rest of the components. Another embodimentof the present invention includes a method of generating data on areduced size image of an original image, where the method comprises: (a)decoding codes into which wavelet coefficients are coded; (b) omittingcodes not to be decoded from codes in a sub-band; and (c) decoding codesother than those omitted as not to be decoded.

Another embodiment of the present invention comprises acomputer-readable recording medium storing a program for causing acomputer to execute a method of generating data on a reduced size imageof an original image, where the method includes: (a) selecting, ofwavelet coefficients in a sub-band, wavelet coefficients to be subjectedto an inverse wavelet transform; and (b) performing the inverse wavelettransform on wavelet coefficients, where performing the inverse wavelettransform includes performing the inverse wavelet transform only on thewavelet coefficients selected to be subjected to the inverse wavelettransform with respect to the wavelet coefficients in the sub-band.

Another of the present invention comprises a computer-readable recordingmedium storing a program for causing a computer to execute a method ofgenerating data on a reduced size image of an original image, where themethod includes performing an inverse wavelet transform on waveletcoefficients of a plurality of components, wherein the inverse wavelettransform is performed independently on each of the components with atleast one of the components having a resolution set therefor, theresolution being set different from a resolution set for the rest of thecomponents. Another embodiment of the present invention comprises acomputer-readable recording medium storing a program for causing acomputer to execute a method of generating data on a reduced size imageof an original image, where the method includes: (a) decoding codes intowhich wavelet coefficients are coded; (b) omitting codes not to bedecoded of codes in a sub-band; and (c) decoding codes other than thoseomitted codes.

A description will now be given, with reference to the accompanyingdrawings, of embodiments of the present invention.

First, a description will be given, with respect to the presentinvention, of the reason a decoded image of a desired resolution can begenerated with a reduced amount of processing by performing an inversewavelet transform only on the coefficients that relate to pixels desiredto be finally obtained, focusing on the correspondence between waveletcoefficients and their pixel positions.

In the following description, a vertical direction refers to upward anddownward directions and a horizontal direction refers to rightward andleftward directions in the accompanying drawings.

FIGS. 2 through 5 are diagrams for illustrating a process of performingwavelet transform called a 5×3 transform employed in JPEG 2000two-dimensionally (in the vertical and horizontal directions) on a 16×16monochrome image. FIG. 2 is a diagram showing an original image and acoordinate system therefor. FIG. 3 is a diagram showing an array ofcoefficients after filtering in the vertical direction. FIG. 4 is adiagram showing an array of coefficients after filtering in thehorizontal direction. FIG. 5 is a diagram showing an array ofcoefficients after rearrangement. JPEG 2000 provides two types ofwavelet transform, that is, 5×3 wavelet transform and 9×7 wavelettransform. In the following description, only the 5×3 wavelet transformis given as an example of wavelet transform. The present invention,however, is also applicable to other wavelet transforms including the9×7 wavelet transform.

As shown in FIG. 2, an X-Y coordinate plane is formed on the image withthe horizontal direction being the X-axis, the vertical direction beingthe Y-axis, and the uppermost leftmost point being the origin. The pixelvalue of a pixel having a Y-coordinate value y for an X-coordinate valuex is expressed as P(y) (0≦y≦15). In JPEG 2000, first, with respect toeach X-coordinate value x, high-pass filtering is performed vertically(in the positive direction of the Y-axis) on each pixel having an oddY-coordinate value y (y=2i+1) using its adjacent pixels, so that acoefficient C(2i+1) is obtained. Next, low-pass filtering is performedon each pixel having an even Y-coordinate value y (y=2i) using itsadjacent coefficients, so that a coefficient C(2i) is obtained. Thehigh-pass filtering and the low-pass filtering are given by thefollowing equations (1) and (2), respectively:C(2i+1)=P(2i+1)−└(P(2i)+P(2i+2))/2┘  (1)C(2i)=P(2i)+└(C(2i−1)+C(2i+1)+2)/4┘  (2)where the symbol └x┘ represents a floor function of x that replaces areal number x with the largest of all the integers smaller than or equalto x. In the edge units of the image, a pixel in the center may lack anadjacent pixel. In this case, an appropriate pixel value is supplementedin accordance with a predetermined rule, which is irrelevant to theessence of the present invention so that a description thereof will beomitted.

If, for the purpose of simplification, the coefficients obtained byhigh-pass filtering are expressed as H, and the coefficients obtained bylow-pass filtering are expressed as L, then a coefficient array 1 ofFIG. 2 is converted to a coefficient array 2 of H and L coefficients asshown in FIG. 3 by the above-described vertical conversion.

Next, high-pass filtering is performed horizontally (in the positivedirection of the X-axis) on each coefficient of an odd X-coordinatevalue x (x=2i+1) using its adjacent coefficients in the coefficientarray 2 of FIG. 3, and then low-pass filtering is performed on eachcoefficient of an even X-coordinate value x (x=2i) using its adjacentcoefficients. This process is performed on each Y-coordinate value y. Inthis case, P(2i), P(2i+1), . . . in the above-described equations (1)and (2) are understood to mean their corresponding coefficients.

If, for the purpose of simplification, the coefficients obtained byperforming low-pass filtering on the above-described coefficients Lusing its adjacent coefficients are expressed as LL, the coefficientsobtained by performing high-pass filtering on the above-describedcoefficients L using its adjacent coefficients are expressed as HL, thecoefficients obtained by performing low-pass filtering on theabove-described coefficients H using its adjacent coefficients areexpressed as LH, and the coefficients obtained by performing high-passfiltering on the above-described coefficients H using its adjacentcoefficients are expressed as HH, then the coefficient array 2 of FIG. 3is converted to a coefficient array 3 of FIG. 4. For purposes of thisdisclosure, a group of coefficients assigned the same symbol (LL, forinstance) is called a sub-band, and the image of FIG. 4 is composed offour sub-bands.

Thus, one wavelet transform operation (one decomposition) is completed.At this point, only the LL coefficients are collected. That is, as acoefficient array 4 of FIG. 5, the coefficients are collected accordingto the sub-bands (LL sub-band 4 ₁, HL sub-band 4 ₂, LH sub-band 4 ₃, andHH sub-band 4 ₄), and only the LL sub-band 4 ₁ is extracted. In sodoing, a half-resolution “image” of the original image is obtained. Suchgrouping by the sub-band is referred to as deinterleaving, while thecoefficients arranged in the state of FIG. 4 are described as“interleaved.” The above-described prior art employs the expression of“scanned and rearranged” to describe the same. The second wavelettransform operation may consider the LL sub-band 4 ₁ as an originalimage and perform the same conversion as described above. In this case,when the coefficients are rearranged, a typical coefficient array 5 (ofLL sub-band 5 ₁, HL sub-band 5 ₂, LH sub-band 5 ₃, HH sub-band 5 ₄, HLsub-band 4 ₂, LH sub-band 4 ₃, and HH sub-band 4 ₄) shown in FIG. 6 isobtained. In the case of FIG. 6, there exist seven types of sub-bandsfrom 2LL to 1HH in total. In FIGS. 5 and 6, the prefix of 1 or 2 appliedto the coefficients indicates the number of wavelet transform operationsby which the coefficients are obtained. This number is referred to as adecomposition level. The levels in FIG. 1 refer to the decompositionlevels. A sub-band of a higher decomposition level has a lowerresolution.

In the above description, in the case of performing a wavelet transformonly one-dimensionally, the wavelet transform may be performed in eithera horizontal or a vertical direction.

On the other hand, inverse wavelet transform is performed by firstperforming inverse low-pass filtering horizontally on each coefficientof an even X-coordinate value x (x=2i+1) using its adjacent coefficientsand then performing inverse high-pass filtering on each coefficient ofan odd X-coordinate value x (x=2i) using its adjacent results of inverselow-pass filtering in the interleaved coefficient array 3 shown in FIG.4. This process is performed on each Y-coordinate value y. The inverselow-pass filtering and the inverse high-pass filtering are given by thefollowing equations (3) and (4), respectively:P(2i)=C(2i)−└(C(2i−1)+C(2i+1)+2)/4┘  (3)P(2i+1)=C(2i+1)+└(P(2i)+P(2i+2))/4┘  (4)

As in the above-described case of a wavelet transform, in the edge unitsof the image, a pixel in the center may lack an adjacent pixel. In thiscase, an appropriate pixel value is supplemented in accordance with apredetermined rule, which is irrelevant to the essence of the presentinvention so that a description thereof will be omitted.

In this manner, the coefficient array 3 of FIG. 4 is converted to thecoefficient array 2; that is, the coefficient array 3 is inverselyconverted. Likewise, successively thereafter, inverse low-pass filteringis performed vertically on each coefficient of an even Y-coordinatevalue y (y=2i) using its adjacent coefficients, and then, inversehigh-pass filtering is performed on each coefficient of an oddY-coordinate value (y=2i+1) using its adjacent results of inverselow-pass filtering. This process is performed on each X-coordinate valuex. In so doing, one inverse wavelet transform operation is completed, sothat the coefficient array 2 of FIG. 3 is returned to the coefficientarray 1 of the image of FIG. 2. That is, the coefficient array 1 of theoriginal image is restructured. When a plurality of wavelet transformoperations are performed, the same inverse wavelet transform operationmay be repeated using the HL and other coefficients, considering thecoefficient array 1 of FIG. 2 as the LL sub-band. An exemplarydescription of the way each sub-band is generated and restructured bywavelet transform and inverse wavelet transform will be given later (seeFIG. 10).

At this point, it can be understood that the result of inverse low-passfiltering is obtained from three coefficients including a coefficientfrom the filtering center (that is, a coefficient desired to besubjected to filtering), and it can also be understood that the resultof inverse high-pass filtering is obtained from a coefficient from thefiltering center and the two adjacent results of inverse low-passfiltering. The two results of inverse low-pass filtering are calculatedfrom five coefficients including the coefficient from the filteringcenter. Therefore, the result of inverse high-pass filtering is obtainedfrom five coefficients. As is apparent from the above-describedunderstanding, in order to obtain one pixel, it is sufficient to performan inverse wavelet transform centered on the target pixel, and it is notnecessary to perform inverse wavelet transform on pixels irrelevant tothe inverse wavelet transform on the target pixel. Accordingly, byperforming an inverse wavelet transform using only those required tofinally obtain a desired pixel of all of the coefficients in the samesub-band, a decoded image of a desired resolution can be generated witha reduced amount of processing without obtaining pixels to besubtracted.

FIG. 7 is a block diagram showing an image data generator 10 accordingto a first embodiment of the present invention.

The image data generator 10 of this embodiment includes an inversewavelet transform unit 11 and a coefficient selecting unit 12. Theinverse wavelet transform unit 11 performs inverse wavelet transform onwavelet coefficients obtained by performing wavelet transform on anoriginal image one or a plurality of times, so that the image datagenerator 10 generates data on a reduced size image of the originalimage. The original image includes an image obtained after performingconversion such as color conversion on the original image.

The coefficient selecting unit 12 selects those to be subjected toinverse wavelet transform of the coefficients in the same sub-band. Inother words, all of the coefficients before selection can also bedefined as all of the coefficients in one LL sub-band, which may be dataon the original image. That is, the LL sub-band may be four sub-bandshaving a decomposition level higher than that of the LL sub-band by one.The selecting operation in this embodiment is different from theconventional technique of, for instance, selecting 2LL, 2HL, 2LH, and2HH sub-bands but not selecting (that is, not performing inverse wavelettransform on) 1HL, 1LH, and 1HH sub-bands. Practically, as will be laterdescribed, the selecting operation can be performed more simply if thecoefficients before selection are interleaved.

The inverse wavelet transform unit 11 performs inverse wavelet transformonly on the coefficients selected by the coefficient selecting unit 12from the above-described wavelet coefficients in the same sub-band. Inthis manner, data on the reduced size image is generated. For instance,in the case of performing an inverse wavelet transform on thecoefficients selected from the coefficients in the 2LL sub-band (thatis, 3LL, 3HL, 3LH, and 3HH sub-bands) using the selective inversewavelet transform of one embodiment of the present invention, thewavelet coefficients relating to other operations including an operationpreceding the inverse wavelet transform, such as coefficients in the 3LLsub-band (composed of 4LL, 4HL, 4LH, and 4HH sub-bands and not processedthrough the coefficient selecting unit 12) to be obtained as required inthe preceding operation may be inversely converted by the inversewavelet transform unit 11.

As described above, it may also be considered that the image datagenerator 10 according to this embodiment includes a unit to selectivelysubject coefficients in the same or a single sub-band to inverse wavelettransform. Here, the sub-band may be the entire original image.

In the specification, coefficients to be inversely converted (orsubjected to inverse wavelet transform) by the inverse wavelet transformunit 11 are referred to as wavelet coefficients or simply ascoefficients. Coefficients to be again inversely converted after beingsubjected to an inverse wavelet transform are also referred to aswavelet coefficients or simply as coefficients. In the case oftwo-dimensional inverse wavelet transform, coefficients to be subjectedto an inverse wavelet transform in both directions and coefficients tobe subjected to an inverse wavelet transform in one direction are alsoreferred to as wavelet coefficients or simply as coefficients.

FIG. 8A is a diagram showing a 16×16 image generated by performinginverse wavelet transform on all of the coefficients obtained afterperforming 5×3 wavelet transform on the original image of FIG. 2.

For purposes of this disclosure, the size of the original image isdefined as 16×16, and a 1/3 scale image, or an image reduced to onethird of the original image vertically and horizontally in size, isgenerated from the original image as previously described in the firstprior art and the second prior art. For purposes of this disclosure, the1/3 scale image is a 5×5 image since 16 is not divisible by three. FIG.8A shows a coefficient array (equal to the coefficient array 1 of FIG.2) of the 16×16 image generated by subjecting all of the coefficients toan inverse wavelet transform first horizontally and then vertically. Inorder to generate a 5×5 image, an inverse wavelet transform may beperformed centered only on the coefficients of the underlined pixels ofall of the coefficients in FIG. 8A. This embodiment employs a 5×3transform, so that the result of vertical inverse high-pass filteringcan be obtained from a coefficient of the filtering center and its twoadjacent results of inverse low-pass filtering. Therefore, finally, itis sufficient to (vertically) perform inverse wavelet transform only forthe 45 shaded pixels in FIG. 8A. Pixels to be obtained in the case ofemploying a 5×3 transform and performing three-to-one scaling as in thisembodiment are the 25 underlined pixels, so that at the preceding stage,that is, at the stage after performing horizontal filtering (beforevertical filtering) at the time of an inverse wavelet transformoperation, it is sufficient that only the 45 shaded pixels have beenobtained. This means that it is sufficient to select pixels equivalentto less than 18% of the entire image and obtain the coefficients of the25 pixels by vertical filtering at the time of an inverse wavelettransform operation. The 45 pixels shown shaded herein do not have thecoefficients shown in FIG. 8A before the vertical inverse wavelettransform. The coefficient values in the pixel positions illustrated inFIG. 8A are obtained only after performing an inverse wavelet transformhorizontally and vertically. According to this embodiment, a reducedsize image can be generated with a reduced amount of calculation.

Additionally, in order to generate a 5×4 image from the 16×16 image, aninverse wavelet transform may be performed centered only on thecoefficients of the underlined pixels of all of the coefficients in FIG.8B. This embodiment employs a 5×3 transform, so that the result ofvertical inverse high-pass filtering can be obtained from a coefficientfrom the filtering center and its two adjacent results of inverselow-pass filtering. Therefore, finally, it is sufficient to (vertically)perform inverse wavelet transform only for the 20 shaded pixels in FIG.8B. This means that it is sufficient to select pixels equivalent to lessthan 8% of the entire image and obtain the coefficients of the 20 pixelsby vertical filtering at the time of an inverse wavelet transformoperation.

The coefficient selecting unit 12 may include a unit to select at leastall of the wavelet coefficients relating to the pixels of a reduced sizeimage to be generated (or desired to be finally obtained). Further, thecoefficient selecting unit 12 may include a unit to select only thewavelet coefficients relating to the pixels of a reduced size image tobe generated (or desired to be finally obtained). That is, the inversewavelet transform may be performed only on the wavelet coefficientsrelating to the pixels of a reduced size image desired to be obtained.For purposes of this disclosure, the term “relating” refers to arelationship originating from the nature of wavelet transforms, such asa relationship derived from the above-described equations (1) through(4) (the shaded pixels to the underlined pixels in FIG. 8A). Accordingto this configuration, a reduced size image can be generated with thesmallest amount of calculation.

It should be noted that an image obtained as a result of performing aninverse wavelet transform only on the coefficients relating to thepixels of a reduced size image desired to be obtained is mathematicallyequivalent to a reduced size image generated by thinning out or reducingan image obtained by performing an inverse wavelet transform on all ofthe wavelet coefficients. In the case of thinning out the waveletcoefficients themselves and performing an inverse wavelet transform onthe remaining wavelet coefficients, a reduced size image of the samesize can be obtained. In this case, however, the inverse wavelettransform is performed using coefficients different from those obtainedin the “forward” wavelet transform. Therefore, the obtained reduced sizeimage has no mathematical grounds.

On the other hand, according to one embodiment of the present invention,a totally equivalent image having mathematical grounds can be obtained.

As previously described, in order to obtain the underlined 25 pixels ofFIG. 8A, in addition to the 25 pixels, the shaded pixels surrounding the25 pixels have also been obtained as the coefficients in the state wherehorizontal filtering is completed (before vertical filtering) at thetime of an inverse wavelet transform operation. If it is difficult todetermine whether a pixel corresponds to the “surrounding pixel,” allthe pixels in each vertical straight line (column) including anunderlined pixel may be selected.

Accordingly, all of the coefficients positioned on a straight lineextending in one direction (in which the inverse wavelet transform isperformed in an inverse wavelet transform operation) where the straightline includes a coefficient corresponding to a pixel position of areduced size image desired to be generated may be obtained. Thecoefficient selecting unit 12 may include a unit to select, of theabove-described wavelet coefficients in the same sub-band (in theinterleaved state), all of the coefficients positioned on a straightline extending in one direction (in the vertical direction in theabove-described case) in which an inverse wavelet transform isperformed, the straight line including a wavelet coefficient in aposition of a pixel of a reduced size image desired to be generated. Bythis selecting operation, all of these selected wavelet coefficients aresubjected to an inverse wavelet transform in the inverse wavelettransform unit 11, and as a result of this inverse wavelet transform,all of the coefficients positioned on each of the above-describedstraight lines including the coefficients of the pixel positions of thereduced size image desired to be generated. The pixels composed of theobtained coefficients are thinned out as appropriate as described above,so that the desired reduced size image is obtained. According to thisconfiguration, the actual application can be simplified in generating areduced size image.

FIG. 9A is a diagram showing a 16×16 image generated by performinghorizontal filtering, at the time of an inverse wavelet transformoperation, on all of the coefficients obtained after performing 5×3wavelet transform on the original image of FIG. 1. A coefficient array 7of FIG. 9A corresponds to the coefficient array 2 of FIG. 3. FIG. 9B isa diagram showing the 16×16 image of FIG. 9A in the case of obtainingits 5×4 image.

In order to obtain the coefficients of the shaded pixel positions ofFIG. 8A, the pixels of the shaded units of FIG. 9A are selected as thecoefficients in the state before horizontal filtering is performed atthe time of an inverse wavelet transform operation. The 126 shadedpixels shown in FIG. 9A do not have the coefficients shown therein,which are obtained only after horizontal filtering at the time of aninverse wavelet transform operation. As in the above-described case, theactual application may also be simplified without making a determinationas to the “surrounding pixels” in the case of FIG. 9A. Likewise, inorder to obtain the underlined 20 pixels of FIG. 8B, in addition to the20 pixels, the shaded pixels surrounding the 20 pixels in FIG. 9B arealso obtained as the coefficients in the state where horizontalfiltering is completed (before vertical filtering) at the time of aninverse wavelet transform operation. If it is difficult to determinewhether a pixel corresponds to the “surrounding pixel,” all the pixelsin each vertical straight line (column) including an underlined pixel inFIG. 9B may be selected to simplify the implementation.

Accordingly, an inverse wavelet transform may be performedtwo-dimensionally, and all of the coefficients positioned on straightlines perpendicular to the direction in which the first inverse wavelettransform in an inverse wavelet transform operation is performed may beobtained, where the straight lines include the coefficientscorresponding to the positions of the pixels of the reduced size imageand the positions relating to the positions of the pixels. Thecoefficient selecting unit 12 of this embodiment may include a unitthat, at the time of selecting coefficients for inverse wavelettransform performed in one direction (in the horizontal direction in theabove-described case) in which the inverse wavelet transform isperformed first in an inverse wavelet transform operation, selects, ofthe above-described wavelet coefficients in the same sub-band (in theinterleaved state), all of the coefficients on straight linesperpendicular to the direction in which the inverse wavelet transform isperformed first, where the straight lines include the coefficientscorresponding to the positions of the pixels of the reduced size imageto be generated and the positions of pixels necessary for obtaining thepositions of the pixels of the reduced size image. As a result ofemploying this unit of the coefficient selecting unit 12, the selectedcoefficients are subjected to an inverse wavelet transform in thedirection in which the inverse wavelet transform is performed first, andare subjected to an inverse wavelet transform in the other direction andthinned out as required. In so doing, the coefficients of the pixelpositions of the reduced size image desired to be generated areobtained. According to this configuration, the actual application can besimplified in generating a reduced size image.

In FIG. 1 of the second prior art, an image having the same resolutionas the original image is first generated and then reduced to one thirdof the original image. In principle, however, it takes less time toobtain a one-third image based on the 1/2-resolution image of theoriginal image. FIG. 10 is a diagram showing a configuration forgenerating a 1/3-resolution image along the flow of a wavelet transformand an inverse wavelet transform according to one embodiment of thepresent invention. In the case of generating a 1/3-resolution image, theLL coefficients of a resolution lower than a desired resolution, thatis, the 2LL coefficients of a one-fourth resolution, may be obtained byperforming an inverse wavelet transform. Then, the obtained 2LLcoefficients are selectively subjected to inverse wavelet transformusing the coefficients of the 2HL, 2LH, and 2HH sub-bands, so that a1/3-resolution image can be finally obtained.

Therefore, according to one embodiment of the present invention, aninverse wavelet transform may be performed on all of the coefficients ofup to the resolution closest to a desired resolution. That is, thecoefficient selecting unit 12 of one embodiment of the present inventionmay include a unit that selects all of the wavelet coefficients in thesub-bands of the same decomposition level higher than that of the LLsub-band having the highest resolution below the resolution of a reducedsize image to be obtained so that the LL sub-band is obtained by aninverse wavelet transform.

As shown in the shaded units of FIG. 8A, in the above-described 5×3transform, the number of adjacent pixels to be obtained differsdepending on whether an underlined pixel desired to be finally obtainedis located in an odd or even position. As previously described, thisresults from the difference in tap length between the low-pass filterand the high-pass filter. In this case, therefore, by selecting pixelsdesired to be finally obtained so that the desired pixels are located ineven positions as much as possible, the number of adjacent pixels to beobtained can be reduced, so that processing can be performed at highspeed. In order to select pixels desired to be finally obtained so thatthe desired pixels are located in even positions, a vertex pixel of thepixels desired to be obtained, that is, the pixel of −3 in FIG. 8A, maybe located in an even position. There is also an alternate method of notarranging the underlined pixels regularly in a grid-like manner.

Therefore, according to one embodiment of the present invention, thecoefficients of pixels in such positions as to reduce the sum of the taplengths of the filters may be selected. In FIG. 8A, in the case ofselecting a position whose X-coordinate and Y-coordinate values are botheven numbers, the tap length for the inverse wavelet transform perdirection becomes Tlow, namely, a minimum length. On the other hand, inthe case of selecting a position whose X-coordinate and Y-coordinatevalues are both odd numbers, the tap length for the inverse wavelettransform per direction becomes Thigh, namely, a maximum length.Accordingly, in order to reduce the amount of processing, it iseffective to select a position so that the tap length for an inversewavelet transform per direction becomes smaller than the average of theminimum and maximum values, that is, (Tlow+Thigh)/2. The high-passfilter and the low-pass filter may have different tap lengths forinverse wavelet transform, so that the sum of the tap lengths of thehigh-pass and low-pass filters that perform filtering centered on thecoefficients corresponding to the pixel positions of a reduced sizeimage to be generated of all of the above-described coefficients in thesame sub-band (in the interleaved state) is smaller thand·n(Tlow+Thigh)/2, where d is the dimensional number of the inversewavelet transform, n is the number of pixels of the reduced size image,Tlow is the tap length of the low-pass filter, and Thigh is the taplength of the high-pass filter. According to this configuration,processing can be performed at high speed in generating a reduced sizeimage by the inverse wavelet transform.

In the case of performing inverse wavelet transform two-dimensionally,the operation of performing an inverse wavelet transform selectively onthe coefficients in the same (or a single) sub-band, and the operationof causing the sum of the tap lengths of the high-pass and low-passfilters to be smaller than n(Tlow+Thigh), the high-pass and low-passfilters having different tap lengths for an inverse wavelet transformand performing filtering centered on the coefficients corresponding tothe pixel positions of a reduced size image of all of the coefficientsin the interleaved state may be provided. In the case of generating areduced size image by performing the inverse wavelet transformtwo-dimensionally, processing can also be performed at high speed.

In the case of generating the 1/3-resolution reduced size image of anoriginal image from wavelet coefficients divided into 3LL, 3HL, 3LH,3HH, 2HL, 2LH, 2HH, 1HL, 1LH, and 1HH sub-bands, using theabove-described configurations suitably, the following processes (a)through (c) may be performed as main procedures to which the selectiveinverse wavelet transform of one embodiment of the present invention isapplied. In the case of performing an inverse wavelet transform ontwo-dimensional coefficients in the horizontal and vertical directions,it may be determined based on the direction in which the inverse wavelettransform is performed whether the selective inverse wavelet transformof one embodiment of the present invention is employed.

(a) The conventional inverse wavelet transform, which does not employthe selective inverse wavelet transform of one embodiment of the presentinvention, that is, which selects all of the coefficients, is performedon the coefficients of the 2LL sub-band, that is, the coefficients ofthe four sub-bands of decomposition level 3 (3LL, 3HL, 3LH, and 3HH). Bydoing so, the 2LL sub-band is obtained. Then, the coefficients of the1LL sub-band, that is, the coefficients of the four sub-bands ofdecomposition level 2 (2LL, 2HL, 2LH, and 2HH) in the interleaved state,are selectively subjected to the inverse wavelet transform, so that anew LL sub-band is extracted. In this manner, a reduced size image isobtained.

(b) Coefficients are selected, in consideration of two inverse wavelettransform operations, from the coefficients of the 2LL sub-band, thatis, the coefficients of the four sub-bands of decomposition level 3(3LL, 3HL, 3LH, and 3HH), in the interleaved state, and the selectedcoefficients are subjected to an inverse wavelet transform twice usingthe coefficients of the 2HL, 2LH, and 2HH sub-bands. In this manner, areduced size image is obtained.

(c) The selection of coefficients in each of the processes (a) and (b)is simplified, and the unnecessary coefficients after the inversewavelet transform operations are subtracted so that a reduced size imageis obtained.

In the case of compressing an original image, which is, for instance, acolor image formed of three components of R, G, and B, normally, inorder to increase the compression rate, color conversion is performed onthe R, G, and B components so that the R, G, and B components areconverted to three new components of one luminance and two colordifferences, and a wavelet transform is performed on each of the newcomponents obtained after the color conversion.

A color conversion called RCT (Reversible Component Transform), which isone of color conversion methods employed in JPEG 2000, is given by thefollowing:

$\begin{matrix}\begin{matrix}{{{{Luminance}\mspace{20mu} Y} = \left\lfloor {\left( {R + {2G} + B} \right)/4} \right\rfloor}\mspace{11mu}} \\{{{{Color}\mspace{14mu}{difference}\mspace{14mu}{Cr}} = {R - G}}\mspace{76mu}} \\{{{{Color}\mspace{14mu}{difference}\mspace{14mu}{Cb}} = {B - G}}\mspace{76mu}}\end{matrix} & (5)\end{matrix}$

The inverse conversion of RCT is given by the following:

$\begin{matrix}\begin{matrix}{{R = {G + {Cr}}}\mspace{110mu}} \\{G = {Y - \left\lfloor {\left( {{Cr} + {Cb}} \right)/4} \right\rfloor}} \\{{B = {{Cb} + G}}\mspace{124mu}}\end{matrix} & (6)\end{matrix}$

FIG. 11 is a block diagram for illustrating an image data generatoraccording to a second embodiment of the present invention and forillustrating a DWT (Discrete Wavelet Transform) image compression anddecompression algorithm in JPEG 2000.

JPEG 2000 is an image compression and decompression method standardizedinternationally in 2001 as a successor to JPEG. The image data generatorof FIG. 11 includes a two-dimensional wavelet transform and inversetransform unit 22, a quantization and inverse quantization unit 23, andan entropy coding and decoding unit 24. Of these units, thetwo-dimensional wavelet transform and inverse transform unit 22 relatesto one embodiment of the present invention. In the specification, thetwo-dimensional wavelet transform and inverse transform unit 22 isdescribed mainly as an inverse wavelet transform unit. Thetwo-dimensional wavelet transform and inverse transform unit 22, thequantization and inverse quantization unit 23, and the entropy codingand decoding unit 24 are provided as a unit receive an input from andtransmit an output to a color space conversion and inverse conversionunit 21 and a tag processing unit 25. Each of these units may haveindependent configurations for the forward (compression) and inverse(decompression) operations. Further, each of these units may performprocessing component by component. At the time of performingdecompression in the JPEG 2000 configuration of FIG. 11, the waveletcoefficients of each of the components obtained through entropy decodingand inverse quantization are subjected to an inverse wavelet transform.Thereafter, the wavelet coefficients are subjected to a color conversionso as to be returned to the R, G, and B pixel values.

When the effect of each component on image quality is considered,normally, the color-difference components are more quantized in thequantization process of FIG. 11 than the luminance component because,generally, luminance has a greater effect than color difference. Byapplying this technique to the generation of a reduced size image sothat an inverse wavelet transform is performed with the color-differencecomponents having a lower resolution than the luminance component and aninverse color conversion is performed with (virtual) interpolation beingperformed on the color-difference components, a reduced size image canbe generated at high speed with the effect on image quality beingcontrolled. Further, the color differences Cr and Cb do not affect imagequality to exactly the same degree. For instance, experiments show thatthe color difference Cb has a smaller effect than the color differenceCr. Therefore, the color-difference components may have differentresolutions.

Therefore, according to this embodiment, an apparatus for generating areduced size image of an original image by performing an inverse wavelettransform on the wavelet coefficients of a plurality of components mayinclude a unit that performs the inverse wavelet transform on thecomponents to different resolutions so that the resolution differsbetween the components when the inverse wavelet transform is performed.That is, an inverse wavelet transform may be performed with a differencebetween the resolutions of the components. The image data generator ofthis embodiment may be an apparatus for generating data on a reducedsize image of an original image, the apparatus including an inversewavelet transform unit that performs an inverse wavelet transform on thewavelet components of a plurality of components. The inverse wavelettransform unit performs an inverse wavelet transform component bycomponent with the resolution differing between at least one of thecomponents and the rest of the components. According to this embodiment,a reduced size image having a plurality of components can be generatedat high speed with a reduced amount of processing using thecharacteristic between the components.

Moreover, by applying the characteristics of this embodiment to theabove-described first embodiment of the image data generator relating tothe selective inverse wavelet transform, processing speed can be furtherincreased and the actual application can be further simplified.

Further, with respect to each of the wavelet coefficient luminancecomponent and the wavelet coefficient color-difference component of theabove-described plural components, the coefficients of the LL sub-bandhaving the highest resolution below the resolution of a reduced sizeimage to be generated may be obtained. According to this configuration,a reduced size image formed of a plurality of components can begenerated at higher speed with more simplicity.

Further, in the image data generator of this embodiment, theabove-described components may be a luminance component and acolor-difference component, and the luminance component is subjected toan inverse wavelet transform to a resolution higher than a resolution towhich the color-difference component is subjected to an inverse wavelettransform. As a result, the color-difference component has a lowerresolution. According to this configuration, a reduced size image formedof luminance and color-difference components can be generated at higherspeed with a reduced amount of processing while the effect on imagequality is controlled.

Further, according to this embodiment, the above-described componentsmay include two color-difference components, and the twocolor-difference components may be subjected to an inverse wavelettransform to different resolutions. According to this configuration, areduced size image formed of a plurality of components may be generatedat higher speed by setting a lower resolution for one of thecolor-difference components than for the other one of thecolor-difference components, using the characteristic between thecolor-difference components.

Further, in this embodiment, the resolution of the color-differencecomponents may be set to a half of the resolution of the luminancecomponent. Generally, this resolution combination, which corresponds tosub-sampling color difference to one-fourth of luminance, provides agood balance between image quality and processing speed. According tothis configuration, a reduced size image having a plurality ofcomponents can be generated with image quality and processing speedbeing in balance with each other.

The foregoing embodiments are described, focusing on the image datagenerators according to the present invention. Embodiments of thepresent invention can also be realized as an image data generatingmethod including the processing operations performed in the image datagenerators; a program for causing a computer to function as any of theabove-described image data generators or as each unit thereof or aprogram for causing a computer to execute the image data generatingmethod (a computer program with the contents of the processing steps);and a computer-readable recording medium recording the program (acomputer-readable information recording medium recording the contents ofthe processing steps). As is apparent from a later-described embodiment,this image data generating method of the present invention may be usedto generate a reduced size image with a reduced amount of calculationand/or generate a reduced size image at high speed using thecharacteristics between components. Further, one embodiment of thisprogram makes it possible to provide a system that can generate areduced size image with a reduced amount of calculation, can generate areduced size image simply with high image quality, and can generate areduced size image at high speed using the characteristics betweencomponents by the operations corresponding to the above-describedembodiments. Further, one embodiment of this recording medium makes itpossible to provide a system that can generate a reduced size image witha reduced amount of calculation, can generate a reduced size imagesimply with high image quality, and can generate a reduced size image athigh speed using the characteristics between components with theconfigurations corresponding to the above-described embodiments. It isapparent that this program and this recording medium can be realizedeasily based on the later-described embodiment in addition to theabove-described embodiments.

A description will be given of a recording medium storing a program ordata for realizing the image data generating function of the presentinvention according to a third embodiment of the present invention.

Specifically, the recording medium may be any of a CD-ROM, amagneto-optical disk, a DVD-ROM, a FD, a flash memory, and other variousROMs and RAMs. The recording medium is recorded with a program forcausing a computer to execute the functions relating to theabove-described embodiments according to the present invention so as torealize the image data generating function of the present invention. Bydistributing this recording medium, the above-described functions can berealized easily. Then, the image data generating function according toone embodiment, the present invention can be performed by loading therecording medium into an information processing apparatus such as acomputer and causing the information processing apparatus to read outthe program or by storing the program in a recording medium provided inan information processing apparatus and reading out the program asrequired.

An expatiation will be given of the third embodiment of the presentinvention.

FIG. 12 is a block diagram showing an image data generator according tothe third embodiment of the present invention.

According to the image data generator of FIG. 12, a RAM 31, a CPU 32,and an HDD 34 are connected via a data bus 33. In one embodiment, areduced size image is generated from a compressed image of an originalresolution and stored in the HDD 34 using the following process.

In step S201, compressed image data of an original resolution recordedon the HDD 34 is read into the RAM 31 by a command transmitted from theCPU 32. Next, in step S202, the CPU 32 reads the compressed image datarecorded in the RAM 31 only for an amount corresponding to apredetermined resolution, and obtains wavelet coefficients. The CPU 32performs processing on the wavelet coefficients according to oneembodiment of the present invention, thereby generating a reduced sizeimage. In step S203, the CPU 32 writes the generated reduced size imageto another region in the RAM 31. In step S204, the reduced size image isrecorded on the HDD 34 by a command transmitted from the CPU 32.

FIG. 13 is a block diagram showing another image data generatoraccording to the third embodiment of the present invention.

According to the image data generator of FIG. 13, a RAM 35 inside apersonal computer (PC), a CPU 36 inside the PC, an HDD 38, and a monitor39 such as a CRT or LCD monitor are connected via a data bus 39. By aninstruction from a user, a reduced size image is generated at high speedfrom image data of an original resolution and displayed on the monitor39.

In step S211, compressed image data of an original resolution recordedon the HDD 38 is read into the RAM 35 by a command transmitted from theCPU 36. Next, in step S212, the CPU 36 reads the compressed image datarecorded on the RAM 35 only for an amount corresponding to apredetermined resolution, and obtains wavelet coefficients. Then, theCPU 36 performs processing on the wavelet coefficients according to oneembodiment of the present invention, thereby generating a reduced sizeimage. In step S213, the CPU 36 writes the generated reduced size imageto another region in the RAM 35. In step S214, the reduced size image istransmitted to and displayed on the monitor 39 by a command transmittedfrom the CPU 36.

FIG. 14 is a flowchart for illustrating the basic flow of an operationof generating a reduced size image in an image data generator accordingto a fourth embodiment of the present invention. FIG. 15 is a diagramshowing a code configuration according to the fourth embodiment of thepresent invention. FIG. 16 is a diagram showing the relationship betweendecomposition level and resolution level according to the fourthembodiment of the present invention.

A description will be given of the case where a reduced size image isgenerated based on an image defined by the even number of rows of pixelsand the even number of columns of pixels, where the image is compressedin compliance with a JPEG-2000 format using the color conversion of theequations (5) and 5×3 wavelet transform in an image data generatorhaving the above-described configuration according to one embodiment ofthe present invention.

In the operation of generating a reduced size data in this embodiment,first, in step S1, the resolution level of a reduced size image to begenerated is set to (resolution level) r based on a resolution (1/k)specified by a user. It is preferable that the image data generatorinclude a unit that allows the user to specify a desired resolution.Then, in step S2, (resolution level) i is set to zero. In steps S3through S5, i is incremented until i reaches r. During this process, instep S4, the entropy codes of all components are decoded with respect toeach resolution level i. The decoding of the entropy codes is thedecoding of variable length codes, and an MQ-coder is employed for thedecoding in JPEG 2000. Since the decoding of the entropy codes isirrelevant to the point of this embodiment, a description thereof willbe omitted.

FIG. 15 shows the codes of the components arranged in the followingorder: component 0 (luminance), component 1 (color difference Cb), andcomponent 2 (color difference Cr) of resolution 0 (minimum resolution),components 0, 1, and 2 of resolution 1, components 0, 1, and 2 ofresolution 2, . . . . As is well known, in JPEG 2000, the codes of allcomponents can be arranged in the order of resolutions as shown in FIG.15. Therefore, it is possible to extract only the wavelet coefficientsfrom the lowest resolution up to a desired resolution with ease (stepsS1 through S5).

In this specification, the expression of a 1/3 “resolution” isfrequently used, while in JPEG 2000, a quantity called “resolutionlevel” is employed as a quantity similar to “resolution.” The lowestresolution is 0, and the second lowest resolution is 1. FIG. 16 showsthe relationship between decomposition level and resolution level. Each“LL” sub-band takes an exceptional value in this relationship. That is,the resolution level of 3LL is resolution level 0, the resolution levelof 3HL, 3LH, and 3HH is resolution level 1, the resolution level of 2HL,2LH, and 2HH is resolution level 2, and the resolution level of 1HL,1LH, and 1HH is resolution level 3. Further, the resolution level of 2LLis resolution level 1, and the resolution level of 1LL is resolutionlevel 2.

The ratio of the resolution of revolution level r to the resolution ofan original image depends on the maximum value of the decompositionlevel. If the maximum value of the decomposition level is d, theresolution of the wavelet coefficients (sub-band) of resolution level r(r>0) with respect to the original image is 1/2^((d−r+1)). Therefore,the value of r that should be set in step S1 in order to generate a 1/kscale image of the original image is given by:r=d−(log ₂ k−1)  (7)

Accordingly, when the desired resolution (1/k) with respect to theoriginal image is provided by the user, the value of r is calculated bythe equation (7) to be set in step S1. In the case of generating areduced size image having an aspect ratio different from that of itsoriginal image as shown in FIG. 8B, if the resolution of the reducedsize image is specified by a user as 1/kh horizontally and 1/kvvertically with respect to the original image, the smaller of kh and kvis defined as k. Then, r is calculated by the equation (7) to be set instep S1, so that the operation of FIG. 14 is performed.

Normally, the wavelet coefficients are quantized, and therefore, shouldbe inversely quantized before being subjected to an inverse wavelettransform. Therefore, when the decoding is completed in each resolutionlevel i lower than resolution level r (that is, “NO” in step S3), instep S6, all of the decoded wavelet coefficients are inverselyquantized. Thereafter, in step S7, the inversely quantized waveletcoefficients are subjected to a selected inverse wavelet transformoperation. The selected inverse wavelet transform operation of step S7is composed of an LL generating operation performed shown in FIG. 17, ahorizontal pixel position determining and horizontal filtering operationperformed shown in FIG. 19, and a vertical pixel position determiningand vertical filtering operation performed shown in FIG. 21, which willbe described later. Each of the operations of FIGS. 17, 19, and 21according to this embodiment is performed with respect to eachcomponent. In step S8, an inverse color conversion operation isperformed when there are two or more components.

FIG. 17 is a flowchart for illustrating the LL generating operationperformed on each component according to the fourth embodiment of thepresent invention. FIG. 18 is a flowchart for illustrating the operationof FIG. 17 in detail. FIG. 18 illustrates an operation of obtaining thecoefficients of an LL sub-band having a resolution lower than that of areduced size image to be generated.

According to this embodiment, first, in step S11 of FIG. 17, the LLgenerating operation is performed on the luminance Y. Next, in step S12,r is decremented by two (r=r−2), and the LL generating operation isperformed on the color difference Cb. Then, in step S13, r isincremented by one (r=r+1), and the LL generating operation is performedon the color difference Cr. Similarly, when the resolution of luminanceis reduced in the ratio of k:1, the resolution of Cr and the resolutionof Cb are reduced in the ratio of 2k:1 and 4k:1, respectively. Then, asfar as Cr and Cb are concerned, k in FIGS. 20 and 22 are treated as 2kand 4k, respectively.

FIG. 18 shows that by using the wavelet coefficients of four sub-bands,(new) LL coefficients of a decomposition level lower by one than that ofthe four sub-bands are generated. By recursively repeating thisoperation, all of the LL coefficients that have the highest resolutionbelow the desired resolution level r can be obtained. That is, accordingto the LL generating operation performed on each component, in step S14of FIG. 18, i is set to one (i=1). Then, in steps S15 through S17, i isincremented until i reaches r. During this process, in step S16, withrespect to each resolution level i, using an LL sub-band and three HL,LH, and HH sub-bands of resolution level i, inverse wavelet transform isperformed to generate a new LL sub-band for a specified component. Whenthe generation of a new LL sub-band is completed in each resolutionlevel i below resolution level r (that is, “NO” in step S15), in stepS18, the number of vertical pixels (rows) LLheight and the number ofhorizontal pixels (columns) LLwidth of the new LL sub-band are retained.Then, in step S19, the LL generating operation ends. In this manner, allof the wavelet coefficients of the LL sub-band having the highestresolution below the resolution of a reduced size image to be generatedare obtained.

As described in step S12, with respect to the color difference Cb, theLL sub-band is generated using the sub-bands of up to a resolution levellower than that of the luminance Y by two. With respect to the colordifference Cr, the LL sub-band is generated using the sub-bands of up toa resolution level higher than that of the color difference Cb by one.In the case of FIG. 17, the resolution of the color difference Cr is setto a half of the resolution of the luminance Y.

FIG. 19 is a flowchart for illustrating the horizontal pixel positiondetermining and horizontal filtering operation performed on eachcomponent according to the fourth embodiment of the present invention.FIG. 20 is a flowchart for illustrating the operation of FIG. 19 indetail.

According to this embodiment, first, in step S21 of FIG. 19, thehorizontal pixel position determining and horizontal filtering operationis performed on the luminance Y. Next, in step S22, the horizontal pixelposition determining and horizontal filtering operation is performed onthe color difference Cb. Then, in step S23, the horizontal pixelposition determining and horizontal filtering operation is performed onthe color difference Cr.

FIG. 20 shows the operation of obtaining the maximum value p of 2^(n)smaller than k, obtaining the horizontal positions of theabove-described “pixels desired to be finally obtained” with k/p beingemployed as a unit (a horizontal position determining operation), andperforming horizontal filtering on all of the vertical positions of eachof the horizontal positions. Although horizontal filtering is performedon all of the vertical positions, the wavelet coefficients can beselected so as to be selectively subjected to an inverse wavelettransform. This is because the horizontal position determining operationis performed. That is, according to the horizontal pixel positiondetermining and horizontal filtering operation, first, in step S24 ofFIG. 20, the maximum value p of 2^(n) smaller than k is obtained basedon the resolution 1/k specified by the user. Next, in step S25 i is setto zero (i=0). Then, in step S26, a horizontal position xs is determinedby xs=└ik/p┘. Thereafter, in steps S27 and S28, i is incremented untilxs equals 2×LLwidth (xs=2×LLwidth), while step S26 is performed. Duringthis process, in step S29, horizontal filtering is performed on all ofthe vertical positions of each column whose X-coordinate value is xs. Ifthe result of step S27 is “NO”, the operation ends. As stated above,when the aspect ratio of a reduced size image is different from that ofthe original image, if a desired resolution (1/kh horizontally and 1/kvvertically) with respect to the original image is provided by a user,the value of r is calculated by the equation (7) using the smaller of khand kv as k.

At this point, the number of adjacent pixels to be obtained can bereduced by first selecting (0, 0) of FIG. 2, that is, a horizontally andvertically even-numbered position, as the “vertex pixel of the pixelsdesired to be finally obtained” of each component.

FIG. 21 is a flowchart for illustrating the vertical pixel positiondetermining and vertical filtering operation performed on each componentaccording to the fourth embodiment of the present invention. FIG. 22 isa flowchart for illustrating the operation of FIG. 21 in detail.

According to this embodiment, first, in step S31, the vertical pixelposition determining and vertical filtering operation is performed onthe luminance Y. Next, in step S32, the vertical pixel positiondetermining and vertical filtering operation is performed on the colordifference Cb. Then, in step S33, the vertical pixel positiondetermining and vertical filtering operation is performed on the colordifference Cr.

The vertical pixel position determining and vertical filteringoperation, which is similar to the horizontal pixel position determiningand horizontal filtering operation of FIGS. 19 and 20, is performed onlyon necessary pixel positions. As previously described, the necessity ofa pixel is determined based on whether the vertical position of thepixel is even-numbered or odd-numbered. That is, according to thisembodiment, first in step S41, i and j are set to zero (i=j=0). Then, instep S42, a horizontal position xs is determined by xs=└ik/p┘. In stepS43, it is determined whether xs<2×LLwidth holds. If xs<2×LLwidth (thatis, “YES” in step S43), steps S44 and S45 (will be later described) areperformed. In the case of “NO” in step S45, in step S46, i isincremented by one and j is set to zero (j=0). If xs≧2×LLwidth (that is,“NO” in step S43), the operation ends. In step S44, a vertical positionys is determined by ys=└jk/p┘. In step S45, it is determined whetherys<2×LLheight holds. If ys<2×LLheight (that is, “YES” in step S45),steps S48 and S49 (will be later described) are performed, and in stepS47, j is incremented by one (j=j+1), and the operation returns to stepS44. This process continues until ys equals 2×LLheight. If ys≧2×LLheight(that is, “NO” in step S45), in step S46, i is incremented by one and jis set to zero (j=0), and the operation returns to step S42. In stepS48, vertical filtering is performed only on each pixel position whoseY-coordinate value is ys. In step S49, each pixel value after thefiltering is stored in the position (i, j) in a buffer for reducedcomponent. Thereafter, as previously described, step S47 is performed.In FIG. 22, the operation of obtaining xs may be omitted. In this case,the vertical filtering is performed with respect to each horizontalposition (column). Besides, when the aspect ratio of a reduced sizeimage is different from that of the original image, if a desiredresolution (1/kh horizontally and 1/kv vertically) with respect to theoriginal image is provided by a user, the horizontal position xs isdetermined by xs=└ikh/p┘ in step S42 and the vertical position ys isdetermined by ys=└jkv/p┘ in step S44.

FIG. 23 is a diagram for illustrating the inverse color conversionoperation according to this embodiment.

The maximum value of the decomposition level and the number of verticalpixels (height) and the number of horizontal pixels (width) of anoriginal image can be read from the headers of the codes, and the numberof vertical pixels and the number of horizontal pixels of a reduced sizeimage to be generated are given by └height/k┘ and └width/k┘,respectively, and also used in the inverse color conversion operation.The color difference components are subjected to an inverse wavelettransform only up to resolutions lower than that of the luminancecomponent by one or more levels. Therefore, the number of pixels of thereduced size image to be generated is defined by the following:

Color difference Cb:

Vertical pixels └height/4k┘,

Horizontal pixels └width/4k┘

Color difference Cr:

Vertical pixels └height/2k┘,

Horizontal pixels └width/2k┘

Similarly, when the aspect ratio of a reduced size image is differentfrom the original image, the number of pixels of the reduced size imageto be generated is defined by the following:

Color difference Cb:

Vertical pixels └height/4kv┘,

Horizontal pixels └width/4kh┘;

Color difference Cr:

Vertical pixels └height/2kv┘,

Horizontal pixels └width/2kh┘

In the inverse color conversion operation, if i<└height/k┘ andj<└width/k┘, later-described steps S55 through S59 are performed. Thatis, first, in step S51 of FIG. 23, i and j are zero (i=j=0). Then, (inthe case of “YES” in step S52) in step S54, i is incremented by oneuntil i equals └height/k┘ with j being set to zero (j=0). During thisoperation, below-described operations are performed, and if it isdetermined in step S52 that i≧└height/k┘, the operation ends. Theoperations performed during the above-described operation are asfollows. In the case of “YES” in step S53, steps S55 through S59 areperformed until j equals └width/k┘. If it is determined in step S53 thatj≧└width/k┘ (that is, “NO” in step S53), i is incremented and j is setto zero (j=0), and the operation returns to step S52. In step S55, withrespect to the luminance Y, Y is determined to be the value of theposition (i, j) in the buffer for reduced component of the luminance Y.In step S56, with respect to the color difference Cb, Cb is determinedto be the value of the position (i/4, j/4) in the buffer for reducedcomponent of the color difference Cb. In step S57, with respect to thecolor difference Cr, Cr is determined to be the value of the position(i/2, j/2) in the buffer for reduced component of the color differenceCr. Next, in step S58, an inverse color conversion is performed by theabove-described equations (6), and in step S59, the R, G, and B valuesare stored in the position (i, j) in a buffer for reduced size image.

As previously described, in the case of obtaining the 1/3-resolutionimage of an original image, the wavelet coefficients of up to an LLsub-band (and HL, LH, and HH sub-bands) that may be interleaved to havea resolution (or pixels) half the resolution (or pixels) of the originalimage are obtained, and the 2/3-resolution image of the interleavedcoefficients of the LL sub-band is generated by the processing describedherein.

FIGS. 24A and 25A are diagrams showing pixels to be obtained in the caseof generating the 2/3-resolution image of the interleaved coefficients.In FIG. 24A, those pixels in the state after horizontal filtering at thetime of an inverse wavelet transform operation are indicated by shading.In FIG. 25A, those pixels in the state after vertical filtering at thetime of the inverse wavelet transform operation are indicated byshading. Further, in FIGS. 24A and 25A, the pixels to be obtained areshown underlined as in FIG. 8A. In a coefficient array 8 of FIG. 24A anda coefficient array 9 of FIG. 25A, as in FIGS. 9A and 8A, the“coefficient positions to be obtained” are indicated by shading as thestate after horizontal filtering and the state after vertical filtering,respectively, at the time of the inverse wavelet transform operation.The coefficient values of FIGS. 24A and 25A correspond to those of FIGS.3 and 2, respectively. The number of pixels of the original image inFIGS. 24A and 25A is different from that in FIGS. 8A and 9A. FIGS. 24Band 25B show pixels to be obtained in the case of generating a 10×8image of the 16×16 interleaved coefficients (sub-band). In FIG. 24B, thecoefficient positions to be subjected to a horizontal inverse wavelettransform are indicated by shading, and in FIG. 25B, the coefficientpositions to be subjected to vertical inverse wavelet transform areindicated by shading.

The above description is given of the selective inverse wavelettransform operation according to one embodiment of the presentinvention. A description will now be given of an image data generator,an image data generating method, and an image data generating programfor generating decoded image data of a desired resolution (desiredreduced size image data), balancing decoding speed and decoded imagequality by decoding unit of the codes of wavelet coefficients in anentropy decoding unit in generating a reduced size image. A descriptionwill also be given of a recording medium storing such a program.

Decoding is often employed in generating a reduced size image to bedisplayed on a display unit having a small screen. In this case, sincethe display unit is limited in representation performance, the imagequality of the reduced size image itself may not be strictly questioned.Rather, decoding time may become an issue. Further, due to the limitedrepresentation performance of the display unit, the degradation of dataon the reduced size image often cannot be observed visually.

In a method that can make a selection as to not only resolution (band)but also the ratio of codes to be decoded (code-decoding ratio) in anentropy decoding unit, such as JPEG 2000, the entropy decoding ofwavelet coefficients can be performed at high speed by limiting thecode-decoding ratio. In the case of JPEG 2000, since the binaryrepresentation of a wavelet coefficient is decoded bit by bit from MSB(Most Significant Bit) to LSB (Least Significant Bit), decoding imagequality and decoding speed can be improved by selecting an appropriatebit up to which the decoding is to be performed. In the case ofdisplaying an image on a display unit having a limited displaycapability as previously described, it is often the case that it is notnecessary to decode all codes.

FIG. 26 is a block diagram showing an image data generator 40 accordingto this embodiment.

The image data generator 40, which generates data on a reduced sizeimage of an original image, includes a coefficient decoding unit 41decode coded wavelet coefficients and a code omitting unit 42.

The code omitting unit 42 omits, of the codes of the same sub-band, thecodes that are not to be decoded. The coefficient decoding unit 41decodes the codes other than those omitted in the code omitting unit 42.That is, the coefficient decoding unit 41 decodes unit of the codes ofthe same sub-band. As will be later described, the image data generator40 may decode unit of a layer and obtain a reduced size image based onthe decoded data. According to this embodiment, it is possible togenerate reduced size data, balancing decoding speed and decoded imagequality. The partial decoding according to one embodiment of the presentinvention excludes the case of performing no decoding, which case isequivalent to the case of omitting decoding by band restriction.

In realizing the above-described improvements, it is important to reducethe amount of codes to be decoded while controlling the effect on imagequality. It is well known that in the case of a wavelet transform, aquantization error generated in coefficients affects image qualitydifferently in each sub-band (each of LL, HL, LH, and HH). The LLsub-band has the largest effect on image quality, and generally,HL≈LH>HH holds in terms of the magnitude of the effect on image quality.Accordingly, normally, the LL sub-band is least quantized while the HHsub-band is most quantized. Further, as in the above-described case ofJPEG 2000, decoding only a number of high-order bit planes (will belater described) with the remaining low-order bit planes being leftundecoded is equivalent to losing lower bits by quantization. This meansthat it is possible to provide a greater code-decoding ratio to the LLsub-band and a smaller code-decoding ratio to the HH sub-band.

Further, it is well know that in the case of a wavelet transform, theeffect of quantization error generated in coefficients on image qualitydiffers depending on the decomposition level. The effect becomes greateras the decomposition level becomes higher.

Therefore, according to this embodiment, the sub-bands may be providedwith different code-decoding ratios. That is, the amount or ratio ofcodes to be omitted (not to be decoded) in the code omitting unit 42 maybe caused to differ among the sub-bands. According to thisconfiguration, by considering the effect on image quality by eachsub-band, a reduced size image can be generated with decoding speed anddecoded image quality being improved.

Further, according to this embodiment, the LL, HL, LH, and HH sub-bandsmay be provided with different code-decoding ratios. That is, the amountor ratio of codes to be omitted in the code omitting unit 42 may becaused to differ among the sub-bands of the same decomposition level.According to this configuration, by considering the effect on imagequality by each of the sub-bands of the same decomposition level, areduced size image can be generated with decoding speed and decodedimage quality beingimproved improved.

Further, according to this embodiment, the decomposition levels may beprovided with different code-decoding ratios. That is, the amount orratio of codes to be omitted in the code omitting unit 42 may be causedto differ among the decomposition levels. According to thisconfiguration, by considering the effect on image quality by eachdecomposition level, a reduced size image can be generated with decodingspeed and decoded image quality being improved.

In the case of compressing an original image, which is, for instance, acolor image formed of three components of R, G, and B, normally, inorder to increase the compression rate, a color conversion is performedon the R, G, and B components so that the R, G, and B components areconverted to three new components of one luminance and two colordifferences, and wavelet transform is performed independently on each ofthe new components obtained after the color conversion.

As previously described, RCT, which is one of color conversion methodsemployed in JPEG 2000, is given by the following:

$\begin{matrix}\begin{matrix}{{{{Luminance}\mspace{20mu} Y} = \left\lfloor {\left( {R + {2G} + B} \right)/4} \right\rfloor}\mspace{11mu}} \\{{{{Color}\mspace{14mu}{difference}\mspace{14mu}{Cr}} = {R - G}}\mspace{76mu}} \\{{{{Color}\mspace{14mu}{difference}\mspace{14mu}{Cb}} = {B - G}}\mspace{76mu}}\end{matrix} & (8)\end{matrix}$

The inverse conversion of RCT is given by the following:

$\begin{matrix}\begin{matrix}{{R = {G + {Cr}}}\mspace{121mu}} \\\left. {G = {Y - {\left\lfloor {{Cr} + {Cb}} \right)/4}}} \right\rfloor \\{{B = {{Cb} + G}}\mspace{124mu}}\end{matrix} & (9)\end{matrix}$where the symbol └x┘ represents a floor function of x that replaces areal number x with the largest of all the integers smaller than or equalto x.

In this case, it is well known that the effect of a quantization errorgenerated in coefficients on image quality differs among the components.In the case of the luminance-color difference system, the luminanceexerts the largest effect. Further, it is also well known that theeffect differs between the color differences. In the case of no colorconversion, the G component has the largest effect.

Therefore, according to one embodiment of the present invention, in anapparatus decoding the wavelet coefficients of a plurality ofcomponents, the components may be provided with different code-decodingratios. That is, decoding may be performed component by component, andthe amount or ratio of codes to be omitted in the code omitting unit 42may be caused to differ among the components. According to thisconfiguration, by considering the effect on image quality by eachcomponent, a reduced size image can be generated with decoding speed anddecoded image quality being improved.

Further, according to this embodiment, the LL sub-band may be providedwith the smallest amount or ratio of codes not to be decoded. Accordingto this configuration, by considering the effect on image quality by theLL sub-band, a reduced size image can be generated with decoding speedand decoded image quality being improved.

Further, according to this embodiment, the HH sub-band may be providedwith the largest amount or ratio of codes not to be decoded. Accordingto this configuration, by considering the effect on image quality by theHH sub-band, a reduced size image can be generated with decoding speedand decoded image quality being improved.

Further, according to this embodiment, a higher decomposition level maybe provided with a smaller amount or ratio of codes not to be decoded.According to this configuration, by considering the effect on imagequality by the decomposition level, a reduced size image can begenerated with decoding speed and decoded image quality being improved.

Further, according to this embodiment, in an apparatus decoding aluminance component, the luminance component may be provided with thesmallest amount or ratio of codes not to be decoded of all components.According to this configuration, by considering the effect on imagequality by luminance, a reduced size image can be generated withdecoding speed and decoded image quality being improved.

Further, according to this embodiment, in an apparatus decoding aplurality of color-difference components, the color-differencecomponents may be provided with different amounts or ratios of codes notto be decoded. According to this configuration, by considering theeffect on image quality by each color-difference component, a reducedsize image can be generated with decoding speed and decoded imagequality being improved.

Further, according to this embodiment, in an apparatus decoding aluminance component Y and two color-difference components Cb and Cr,Y<Cr<Cb may hold in terms of the amount or ratio of codes not to bedecoded. It is empirically known that in light of human visualcharacteristics, Cb has a smaller effect than Cr. According to thisconfiguration, by considering the effect on image quality by each of Cband Cr, a reduced size image can be generated with decoding speed anddecoded image quality being improved.

Normally, in order to generate a reduced size image of a desired size,codes are decoded to a size larger than the desired size and thinned outafter being subjected to an inverse wavelet transform, or codes aredecoded to a size smaller than the desired size and subjected tointerpolation. When these decoding cases are compared at the samedecomposition level (to be subjected to decoding), the code-decodingratio should be set higher in the latter case (with interpolationprocessing) than in the former case (with thinning-out processing).

Therefore, the image data generator 40 of this embodiment may include aunit to decode only a sub-band of a size smaller than or equal to adesired image size. In other words, the codes are extracted in the sizeof an LL sub-band. According to this configuration, by restricting thesize of a sub-band to be decoded, a reduced size image can be generatedwith decoding speed and decoded image quality being improved.

Further, the image data generator 40 of this embodiment may include aunit to decode only a sub-band of a size smaller than a desired imagesize and a unit to thin out the decoded sub-band. According to thisconfiguration, by restricting the size of a sub-band to be decoded, areduced size image can be generated with decoding speed and decodedimage quality being improved.

Further, the image data generator 40 of this embodiment may include aunit to decode sub-bands of up to the maximum of sizes smaller than orequal to a desired image size and a unit to perform interpolation.According to this configuration, by restricting the size of a sub-bandto be decoded, a reduced size image can be generated with decoding speedand decoded image quality being improved.

The above description is given, focusing on the image data generatorperforming the partial decoding of one embodiment of the presentinvention. One embodiment of the present invention may also be realizedas: an image data generating method including the processing stepsperformed in the image data generator; a program for causing a computerto function as the above-described image data generator or as each unitthereof or a program for causing a computer to execute the image datagenerating method (a computer program with the contents of theprocessing steps); and a computer-readable recording medium recordingthe program (a computer-readable information recording medium recordingthe contents of the processing steps). As is apparent from alater-described embodiment, by this image data generating method of thepresent invention, a reduced size image can be generated with decodingspeed and decoded image quality being balanced or improved. Further,this program makes it possible to provide a system that can generate areduced size image, balancing or improving decoding speed and decodedimage quality, by the operations corresponding to the above-describedembodiment. Further, this recording medium makes it possible to providea system that can generate a reduced size image, balancing or improvingdecoding speed and decoded image quality, with the configurationscorresponding to the above-described embodiment. It is apparent thatthis program and this recording medium can be realized easily based onthe later-described embodiment in addition to the above-describedembodiment.

A description will be given of a recording medium storing a program ordata for realizing the image data generating function of the presentinvention according to a sixth embodiment of the present invention.

Specifically, the recording medium may be any of a CD-ROM, amagneto-optical disk, a DVD-ROM, a FD, a flash memory, and other variousROMs and RAMs. The recording medium is recorded with a program forcausing a computer to execute the functions relating to theabove-described embodiment according to the present invention so as torealize the image data generating function of the present invention. Bydistributing this recording medium, the above-described functions can berealized easily. Then, the image data generating function according tothe present invention can be performed by loading the recording mediuminto an information processing apparatus such as a computer and causingthe information processing apparatus to read out the program or bystoring the program in a recording medium provided in an informationprocessing apparatus and reading out the program as required.

A specific description will be given of the partial decoding operationof the present invention.

As will be later described, the amount or ratio of codes not to bedecoded in the partial decoding operation of the present inventionmeans, for instance, the “number of bit planes not to be decoded” or the“number of bit planes not to be decoded against the total number ofcoded bit planes.”

Since this embodiment employs an apparatus configuration equal to thosedescribed with reference to FIGS. 12 and 13, a description thereof willbe omitted.

In this embodiment, JPEG 2000 selecting the 5×3 wavelet transform isemployed. Therefore, a description will first be given of the outline ofthe JPEG 2000 operation. The application range of the present inventionis not limited to JPEG 2000.

Referring again to FIG. 11, the rightward arrow (→) and the leftwardarrow (←) in the JPEG 2000 encoding and decoding processes indicate thedirection of encoding (compression) and the direction of decoding(decompression), respectively. FIG. 11 shows that at the time ofdecoding, the wavelet coefficients of each component obtained throughentropy decoding and inverse quantization (as required) are subjectedcomponent by component to an inverse wavelet transform and then aninverse color conversion to be returned to the R, G, and B pixel values.

Since the color space conversion and inverse conversion unit 21 ispreviously described, a description will now be given of a reduced sizeimage generating operation according to this embodiment while defining“sub-band” and “decomposition level.”

Since a wavelet transform and an inverse wavelet transform themselvesare described with reference to FIGS. 2 through 6, 10, 11, and 15, adescription thereof will be omitted.

A description will be given of the encoding of the wavelet coefficientsof each sub-band. As is well known, in JPEG 2000, it is possible to codethe coefficients from MSB to LSB in bit planes in each sub-band.Strictly, the encoding is performed by subdividing each bit plane, adescription of which is omitted.

FIG. 27A is a diagram showing the coefficients of a 2LL sub-band, andFIG. 27B is a diagram showing the coefficients divided into bit planes.FIG. 28 is a diagram showing a code configuration according to the sixthembodiment. FIG. 28 shows that codes can be arranged in the order thecodes are arranged from top to bottom in FIG. 28.

For purposes of this application, it is supposed that the coefficientsof the 2LL sub-band 5 ₁ of FIG. 6 take the values shown in FIG. 27A.These values are expressed in binary numbers and the binary numbers ofthe same digit position are grouped into a bit plane. The coefficientsof FIG. 27A can be divided into the four bit planes of FIG. 27B. Thedecimal number 15 is expressed as a binary 1111, so that a binary 1occupies the position corresponding to 15 in each bit plane.

In JPEG 2000, each bit plane is individually coded. That is, it ispossible to generate codes with the configuration of FIG. 28. FIG. 28shows that the codes start from the 2LL sub-band and end at the 1HHsub-band. The bit planes are coded in order from the MSB bit plane tothe LSB bit plane, and the decoder can recognize the total number ofcoded bit planes. Therefore, the decoder can easily omit the decoding ofthe LSB bit plane or the decoding of the two bit planes counted from theLSB bit plane.

Based on the above, a description will be given of the basic flow of areduced size image generating operation to which the partial decoding ofone embodiment of the present invention is applied.

FIG. 29 is a flowchart for illustrating the basic flow of the reducedsize image generating operation performed in an image data generatoraccording to the sixth embodiment of the present invention. FIGS. 30through 32 are flowcharts for expatiating the partial decoding in theoperation of FIG. 29, showing the partial decoding in the luminancecomponent Y, the color difference component Cr, and the color differencecomponent Cb, respectively.

A description will be given, with reference to FIGS. 29 through 32, ofan operation of generating a reduced size image based on image datacompressed losslessly using the color conversion of the equations (8)and 5×3 wavelet transform in the image data generator having theconfiguration of FIG. 12 or 13 according to the sixth embodiment of thepresent invention. Since the image data is compressed by losslesscompression, all of the bit planes of all of the sub-bands are coded.

According to the reduced size image generating operation of thisembodiment, first, in step S71 of FIG. 29, the resolution level of areduced size image to be generated is set to (resolution level) r basedon a resolution (1/k) specified by a user. Then, in step S72,(resolution level) i is set to zero (i=0) and r is decreased by one(r=r−1). In steps S73 through S75, i is incremented while i satisfiesi≦r. During this process, in step S74, the entropy codes of allcomponents are decoded with respect to each resolution level i.Additionally, as stated above, when the aspect ratio of a reduced sizeimage is different from that of the original image, if a desiredresolution (1/kh horizontally and 1/kv vertically) with respect to theoriginal image is provided by a user, the value of r is calculated bythe equation (7) using the smaller of kh and kv as k. It is clear thatthe following examples can be modified to the above case easily.

FIG. 28 shows the codes of the components arranged in the followingorder: component 0 (luminance), component 1 (color difference V), andcomponent 2 (color difference U) of resolution 0 (minimum resolution),components 0, 1, and 2 of resolution 1, components 0, 1, and 2 ofresolution 2, . . . . As is well known, in JPEG 2000, the codes of allcomponents can be arranged in the order of resolutions as shown in FIG.28. Therefore, it is possible to extract only the wavelet coefficientsfrom the lowest resolution up to a desired resolution with ease (stepsS71 through S75).

In this specification, the expression of a 1/3 “resolution” isfrequently used, while in JPEG 2000, a quantity called “resolutionlevel” is employed as a quantity similar to “resolution.” The lowestresolution is 0, and the second lowest resolution is 1. FIG. 16 showsthe relationship between decomposition level and resolution level. Each“LL” sub-band takes an exceptional value in this relationship. That is,the resolution level of 3LL is resolution level 0, the resolution levelof 3HL, 3LH, and 3HH is resolution level 1, the resolution level of 2HL,2LH, and 2HH is resolution level 2, and the resolution level of 1HL,1LH, and 1HH is resolution level 3. Further, the resolution level of 2LLis resolution level 1, and the resolution level of 1LL is resolutionlevel 2.

The ratio of the resolution of revolution level r to the resolution ofan original image depends on the maximum value of the decompositionlevel. If the maximum value of the decomposition level is d, theresolution of the wavelet coefficients (sub-band) of resolution level r(r>0) with respect to the original image is 1/2^((d−r+1)).Therefore, thevalue of r that should be set in step S71 in order to generate a 1/kscale image of the original image is given by the above-describedequation:r=d−(log₂ k−1)  (7)

Accordingly, when the desired resolution (1/k) with respect to theoriginal image is provided by the user, the value of r is calculated bythe equation (7) to be set in step S71.

Normally, the wavelet coefficients are quantized, and therefore, shouldbe inversely quantized before being subjected to an inverse wavelettransform. Therefore, when the decoding is completed in each resolutionlevel i lower than resolution level r (that is, “NO” in step S73), instep S76, all of the decoded wavelet coefficients are inverselyquantized. Thereafter, in step S77, the inversely quantized waveletcoefficients are subjected to an inverse wavelet transform operation.The above-described selected inverse wavelet transform operation may beapplied as the inverse wavelet transform operation of step S77. Next, instep S78, it is determined whether i equals r. If i does not equal r instep S78, in step S79, thinning-out processing is performed. In the caseof a plurality of components, when i equals r (that is, “YES” in stepS78) or after thinning-out processing (step S79), in step S80, inversecolor conversion is performed and the operation ends.

Partial decoding, which is one feature of one embodiment of the presentinvention, is the operation of step S74. According to this embodiment,the wavelet coefficients of each component are obtained by partiallydecoding the codes of each component in the following manner, dependingon the value of i of the resolution level (or depending on thedecomposition level).

Referring to FIG. 30, first, in step S81, it is determined whether thecomponent is the luminance Y. If the component is other than theluminance Y, the operation of FIG. 31 or 32 is started. With respect tothe luminance Y (that is, in the case of “YES” in step S81), in stepS82, it is determined whether i<r−2 is satisfied, and in step S84, it isdetermined whether i≦r−1 is satisfied. Based on the results ofdetermination of these steps, the codes of the luminance Y are partiallydecoded so that the wavelet coefficients of the luminance Y areobtained.

When i≦r−2 (that is, “YES” in step S82), in step S83, the codes of allof the bit planes are decoded with respect to each sub-band. Since theLL sub-band exists only at resolution level 0, all of the codes of theLL sub-band are decoded as a result of step S83, so that the amount ofcodes not to be decoded is reduced.

When r−2<i≦r−1 (that is, “NO” in step S82 and “YES” in step S84), instep S85, decoding is performed on the bit planes of the sub-bandsexcept for the two bit planes counted from the LSB bit plane (that is,the LSB bit plane and the next low-order bit plane) with respect to theHL and LH sub-bands and the three bit planes counted from the LSB bitplane with respect to the HH sub-band.

When r−1<i≦r (that is, “NO” in step S82 and “NO” in step S84), in stepS86, decoding is performed on the bit planes of the sub-bands except forthe three bit planes counted from the LSB bit plane with respect to theHL and LH sub-bands and the four bit planes counted from the LSB bitplane with respect to the HH sub-band.

With respect to the codes of the color difference Cr, in step S91 ofFIG. 31, it is determined whether the component is the color differenceCr. If the component is other than the color difference Cr, theoperation of FIG. 32 (or 30) is started. With respect to the colordifference Cr (that is, in the case of “YES” in step S91), in step S92,it is determined whether i≦r−3 is satisfied, in step S94, it isdetermined whether i≦r−2 is satisfied, and in step S96, it is determinedwhether i≦r−1 is satisfied. Based on the results of determination ofthese steps, the codes of the color difference Cr are partially decodedso that the wavelet coefficients of the color difference Cr areobtained. With respect to the codes of the color difference Cr, thewavelet coefficients are obtained by further omitting the decoding ofone more bit plane than with respect to the codes of the luminance Y.

When i≦r−3 (that is, “YES” in step S92), in step S93, the codes of allof the bit planes are decoded with respect to each sub-band.

When r−3<i≦r−2 (that is, “NO” in step S92 and “YES” in step S94), instep S95, decoding is performed on the bit planes of the sub-bandsexcept for the two bit planes counted from the LSB bit plane withrespect to the HL and LH sub-bands and the three bit planes counted fromthe LSB bit plane with respect to the HH sub-band.

When r−2<i≦r−1 (that is, “NO” in step S92, “NO” in step S94, and “YES”in step S96), in step S97, decoding is performed on the bit planes ofthe sub-bands except for the three bit planes counted from the LSB bitplane with respect to the HL and LH sub-bands and the four bit planescounted from the LSB bit plane with respect to the HH sub-band.

When r−1<i≦r (that is, “NO” in steps S92, S94, and S96), in step S98,decoding is performed on the bit planes of the sub-bands except for thefour bit planes counted from the LSB bit plane with respect to the HLand LH sub-bands and the five bit planes counted from the LSB bit planewith respect to the HH sub-band.

With respect to the codes of the color difference Cb, in step S101 ofFIG. 32, it is determined whether the component is the color differenceCb. If the component is other than the color difference Cb, theoperation of FIG. 30 or 31 is started. With respect to the colordifference Cb (that is, in the case of “YES” in step S101), in stepS102, it is determined whether i≦r−3 is satisfied, in step S104, it isdetermined whether i≦r−2 is satisfied, and in step S106, it isdetermined whether i≦r−1 is satisfied. Based on the results ofdetermination of these steps, the codes of the color difference Cb arepartially decoded so that the wavelet coefficients of the colordifference Cb are obtained. With respect to the codes of the colordifference Cb, the wavelet coefficients are obtained by further omittingthe decoding of one more bit plane than with respect to the codes of thecolor difference Cr.

When i≦r−3 (that is, “YES” in step S102), in step S103, the codes of allof the bit planes are decoded with respect to each sub-band.

When r−3<i≦r−2 (that is, “NO” in step S102 and “YES” in step S104), instep S105, decoding is performed on the bit planes of the sub-bandsexcept for the three bit planes counted from the LSB bit plane withrespect to the HL and LH sub-bands and the four bit planes counted fromthe LSB bit plane with respect to the HH sub-band.

When r−2<i≦r−1 (that is, “NO” in step S102, “NO” in step S104, and “YES”in step S106), in step S107, decoding is performed on the bit planes ofthe sub-bands except for the four bit planes counted from the LSB bitplane with respect to the HL and LH sub-bands and the five bit planescounted from the LSB bit plane with respect to the HH sub-band.

When r−1<i≦r (that is, “NO” in steps S102, S104, and S106), in stepS108, decoding is performed on the bit planes of the sub-bands exceptfor the five bit planes counted from the LSB bit plane with respect tothe HL and LH sub-bands and the six bit planes counted from the LSB bitplane with respect to the HH sub-band.

Thus, Y<Cr<Cb holds among the components in terms of the amount of codesnot to be decoded. Further, the amount of codes not to be decoded issmaller at a higher decomposition level. When each sub-band has the sametotal number of coded bit planes, the amount of codes not to be decodedis directly equal to the ratio of codes not to be decoded.

In the case of JPEG 2000, an MQ-coder is employed as an entropy coder.In the partial decoding of one embodiment of the present invention, itis important that the code configuration allow partial omission ofdecoding. Since the details of the entropy decoder have no directrelation to that nature of the partial decoding of one embodiment of thepresent invention, a description thereof will be omitted.

Referring back to FIG. 29, if i=r+1 in step S78 (that is, “YES” in stepS78), the resolution specified by the user matches the resolution levelof wavelet transform. Therefore, after performing an inversequantization and an inverse wavelet transform, an inverse colorconversion is performed without thinning-out processing so that adesired reduced size image is generated. On the other hand, if i=r instep S78 (that is, “NO” in step S78), the resolution level of wavelettransform is higher than the resolution specified by the user.Therefore, in step S79, each of Y, Cr, and Cb is converted to a desiredsize by well-known thinning-out processing after being subjected to aninverse quantization and an inverse wavelet transform. In thisembodiment, in order to reduce the amount of processing, thinning-outprocessing is performed before the inverse color conversion instead ofthinning out the R, G, and B values obtained after the inverse colorconversion.

Omitting the decoding of the LSB bit plane is equivalent to dividing(quantizing) the wavelet coefficients by two. Omitting the decoding ofthe n bit planes counted from the LSB bit plane is equivalent toquantizing the wavelet coefficients by 2^(n). Therefore, in the case ofomitting the decoding of bit planes, multiplying the decoded waveletcoefficients by 2^(n) is equivalent to performing an inversequantization on the decoded wavelet coefficients.

In this embodiment, the equations (8) are employed to calculate Y, Cr,and Cb. In the case of calculating Y, Cr, and Cb using the well knownequations provided by CCIR 601, however, the technique of thisembodiment is also applicable. Further, the nearest neighbor method,which is widely used, is taken as an example of thinning-out processing.Since the algorithm of thinning-out processing itself does not affectthe partial decoding of one embodiment of the present invention, anexplanation of the algorithm will be omitted. For the details of thealgorithm, see “Introduction to Computer Image Processing” (by HideyukiTamura, Soken Publishing Ltd., 1985).

FIG. 33 is a flowchart for illustrating the basic flow of anotherreduced size image generating operation performed in the image datagenerator according to this embodiment to which method the partialdecoding of the present invention is applied.

In the above-described case, the conditional expression of step S73 isi≦r. Therefore, the resolution level of the extracted waveletcoefficients is equal to or higher by one than the resolution specifiedby the user. If the conditional expression of step S73 is changed toi<r, however, the resolution level lower than the resolution levelspecified by the user by one can be extracted, so that each of Y, Cr,and Cb is converted to a desired size by well known interpolationprocessing after being subjected to an inverse wavelet transform.

According to the reduced size image generating operation of FIG. 33according to this embodiment, first, in step S111, the resolution levelof a reduced size image to be generated is set to (resolution level) rbased on a resolution (1/k) specified by the user. Then, in step S112,(resolution level) i is set to zero (i=0) and r is decreased by one(r=r−1). In steps S113 through S115, i is incremented while i satisfiesi≦r. During this process, in step S114, the entropy codes of allcomponents are decoded with respect to each resolution level i. As inthe above-described case, the operations described with reference toFIGS. 30 through 32 are applicable to the partial decoding operation onY, Cr, and Cb of step S114.

Normally, the wavelet coefficients are quantized, and therefore, shouldbe inversely quantized before being subjected to an inverse wavelettransform. Therefore, when the decoding is completed in each resolutionlevel i lower than resolution level r (that is, “NO” in step S113), instep S116, all of the decoded wavelet coefficients are inverselyquantized. Thereafter, in step S117, the inversely quantized waveletcoefficients are subjected to an inverse wavelet transform operation.The above-described selected inverse wavelet transform operation may beapplied as the inverse wavelet transform operation of step S117. Next,in step S118, interpolation is performed. The nearest neighbor method,which is widely used, is taken as an example of interpolation. For theexpatiation of the algorithm of interpolation, the above-described“Introduction to Computer Image Processing” may be referred to. In thecase of a plurality of components, in step S119, an inverse colorconversion is performed and the operation ends.

Thus, according to one embodiment of the present invention, the waveletcoefficients are subjected to an inverse wavelet transform, and in thecase of generating a reduced size image of an original image, thewavelet coefficients in the same sub-band are selectively subjected toan inverse wavelet transform. Therefore, the reduced size image can begenerated with a reduced amount of calculation.

Further, according to one embodiment of the present invention, thewavelet coefficients in the same sub-band are partially decoded inperforming an inverse wavelet transform on the wavelet coefficients andgenerating a reduced size image of an original image. Therefore, thereduced size image can be generated with decoding speed and decodedimage quality being balanced with each other.

The present invention is not limited to the specifically disclosedembodiments, but variations and modifications may be made withoutdeparting from the scope of the present invention.

The present application is based on Japanese priority application No.2002-072696 filed on Mar. 15, 2002, the entire contents of which arehereby incorporated by reference.

Whereas many alterations and modifications of the present invention willno doubt become apparent to a person of ordinary skill in the art afterhaving read the foregoing description, it is to be understood that anyparticular embodiment shown and described by way of illustration is inno way intended to be considered limiting. Therefore, references todetails of various embodiments are not intended to limit the scope ofthe claims which in themselves recite only those features regarded asessential to the invention.

1. An apparatus for generating data for a reduced size image of anoriginal image, the apparatus comprising: a coefficient selecting unitto select wavelet coefficients to be subjected to an inverse wavelettransform in a same sub-band from wavelet coefficients obtained byperforming a wavelet transform on the original image one or more times;and an inverse wavelet transform unit to perform the inverse wavelettransform only on the wavelet coefficients selected in the coefficientselecting unit with respect to the sub-band, wherein the coefficientselecting unit selects the wavelet coefficients required to obtaindesired pixels of the original image.
 2. The apparatus as claimed inclaim 1, wherein the coefficient selecting unit comprises a unit toselect at least all of wavelet coefficients relating to pixels of thesize-reduced image to be generated.
 3. The apparatus as claimed in claim1, wherein the coefficient selecting unit comprises a unit to selectonly wavelet coefficients relating to pixels of the size-reduced imageto be generated.
 4. The apparatus as claimed in claim 1, wherein theinverse wavelet transform comprises a plurality of inverse wavelettransforms; and the coefficient selecting unit comprises a unit toselect, of the wavelet coefficients in the sub-band in an interleavedstate, all of wavelet coefficients positioned on straight linesextending in a direction in which the last one of the inverse wavelettransforms is performed, the straight lines each including a waveletcoefficient corresponding to a pixel position of the size-reduced imageto be generated.
 5. The apparatus as claimed in claim 1, wherein: theinverse wavelet transform is performed two-dimensionally in first andsecond directions perpendicular to each other in an order; and thecoefficient selecting unit comprises a unit that, in selecting waveletcoefficients to be subjected to the inverse wavelet transform performedin the first direction, selects, of the wavelet coefficients in thesub-band in an interleaved state, all of wavelet coefficients positionedon straight lines extending in the second direction, the straight linesincluding a wavelet coefficient corresponding to a pixel position of thesize-reduced image to be generated or a wavelet coefficient required toobtain the pixel position by the inverse wavelet transform in the firstdirection.
 6. The apparatus as claimed in claim 1, wherein thecoefficient selecting unit comprises a unit to select all of waveletcoefficients in sub-bands of a decomposition level higher than adecomposition level of an LL sub-band having a maximum resolution belowa resolution of the size-reduced image to be generated, in order toobtain the LL sub-band by the inverse wavelet transform.
 7. Theapparatus as claimed in claim 1, further comprising a high-pass filterand a low-pass filter having different tap lengths for the inversewavelet transform, wherein the sum of the tap lengths of the high-passand low-pass filters performing filtering centered on waveletcoefficients corresponding to pixel positions of the size-reduced imageto be generated of the wavelet coefficients in the sub-band in aninterleaved state is smaller thand·n(Tlow+Thigh)/2 where d is a dimensional number of the inverse wavelettransform, n is the number of pixels of the size-reduced image, Tlow isthe tap length of the low-pass filter, and Thigh is the tap length ofthe high-pass filter.
 8. The apparatus as claimed in claim 1, whereinthe inverse wavelet transform is performed independently on each of aplurality of components with at least one of the components having aresolution set therefor, the resolution being set different from aresolution set for the rest of the components.
 9. The apparatus asclaimed in claim 8, wherein: the components comprises a luminancecomponent and two color-difference components; and the luminancecomponent is subjected to the inverse wavelet transform to a resolutionhigher than the color-difference components.
 10. An image data generatorfor generating data for a reduced size image of an original image, theimage data generator comprising: a coefficient selection unit to selectwavelet coefficients to be subjected to an inverse wavelet transform ina same sub-band from wavelet coefficients obtained by performing awavelet transform on the original image one or more times; an inversewavelet transform unit to perform inverse wavelet transformindependently on each of the components with at least one of thecomponents having a resolution set therefor, the resolution being setdifferent from a resolution set for the rest of the components; whereinthe coefficient selecting unit selects the wavelet coefficients requiredto obtain desired pixels of the original image.
 11. The image datagenerator as claimed in claim 10, wherein: the wavelet coefficients areof a plurality of components: the components comprises a luminancecomponent and two color-difference components; and the luminancecomponent is subjected to the inverse wavelet transform to a resolutionhigher than the color-difference components.
 12. A computer-implementedmethod of generating a reduced size image of an original image, themethod comprising: (a) selecting wavelet coefficients to be subjected toan inverse wavelet transform in a same sub-band from waveletcoefficients obtained by performing a wavelet transform on the originalimage one or more times; and (b) performing the inverse wavelettransform only on the wavelet coefficients selected to be subjected tothe inverse wavelet transform with respect to the sub-band to generatedata of the reduced size image, wherein the coefficient selecting unitselects the wavelet coefficients required to obtain desired pixels ofthe original image.
 13. An article of manufacture having one or morecomputer-readable recording media storing instructions which, whenexecuted by a system, cause the system to generate data for a reducedsize image of an original image by: (a) selecting wavelet coefficientsto be subjected to an inverse wavelet transform in a same sub-band fromwavelet coefficients obtained by performing a wavelet transform on theoriginal image one or more times; and (b) performing the inverse wavelettransform only on the wavelet coefficients selected to be subjected tothe inverse wavelet transform with respect to the sub-band to generatedata of the reduced size image, wherein the coefficient selecting unitselects the wavelet coefficients required to obtain desired pixels ofthe original image.
 14. An apparatus of generating a reduced size imageof an original image, the apparatus comprising: means for selectingwavelet coefficients to be subjected to an inverse wavelet transform ina same sub-band from wavelet coefficients obtained by performing awavelet transform on the original image one or more times; and means forperforming the inverse wavelet transform only on the waveletcoefficients selected to be subjected to an inverse wavelet transformwith respect to the sub-band, wherein the coefficient selecting unitselects the wavelet coefficients required to obtain desired pixels ofthe original image.